<Text-field style="Heading 1" layout="Heading 1">1. Line\303\241ris algebra</Text-field>

restart;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

<Text-field style="Heading 2" layout="Heading 2">1.1. M\303\241trixok \303\251s vektorok</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.1.1. Test.</Text-field>

1,2+2,3^2,3.45/3,Pi,3+4*I,x^2=-1,Alma,infinity,-infinity;

NiwiIiIiIiUiIiokIisrKytdNiEiKkkjUGlHJSpwcm90ZWN0ZWRHLCYiIiRGIyomRiRGI14jRiNGI0YjLyokKUkieEc2IiIiI0YjISIiSSVBbG1hR0YzSSlpbmZpbml0eUdGKiwkRjdGNQ==

evalf(%);

NiwkIiIiIiIhJCIiJUYlJCIiKkYlJCIrKysrXTYhIiokIithRWZUSkYsLCYkIiIkRiVGJComRiZGJF4jRiRGJEYkLyokKUkieEc2IiIiI0YkJCEiIkYlSSVBbG1hR0Y4JEYkSSlpbmZpbml0eUclKnByb3RlY3RlZEckRjtGPg==

%%[5],%%[6];

NiRJI1BpRyUqcHJvdGVjdGVkRywmIiIkIiIiKiYiIiVGJ14jRidGJ0Yn

?Pi

Digits:=50;

IiNd

evalf(Pi);

JCJTXlAqUnByPiUpR116S1FWRVlRS3oqZWBFZlRKISNc

Digits:=10;

IiM1

A:=Alma; Alma:=1; A; Alma:='Alma'; A;

SSVBbG1hRzYi

IiIi

SSVBbG1hRzYi

whattype(1); whattype(1/2); whattype(0.5); whattype(Alma); whattype(infinity);whattype(Pi);whattype(A); whattype(2); whattype(krikszkraksz); whattype("krikszkraksz");

SShpbnRlZ2VyRyUqcHJvdGVjdGVkRw==

SSlmcmFjdGlvbkclKnByb3RlY3RlZEc=

SSZmbG9hdEclKnByb3RlY3RlZEc=

SSdzeW1ib2xHJSpwcm90ZWN0ZWRH

STFleHRlbmRlZF9udW1lcmljRyUqcHJvdGVjdGVkRw==

SSdzeW1ib2xHJSpwcm90ZWN0ZWRH

SShpbnRlZ2VyRyUqcHJvdGVjdGVkRw==

SSdzeW1ib2xHJSpwcm90ZWN0ZWRH

SSdzdHJpbmdHJSpwcm90ZWN0ZWRH

type(1,integer);type(1,float);type(1+3*I,complexcons);

SSV0cnVlRyUqcHJvdGVjdGVkRw==

SSZmYWxzZUclKnByb3RlY3RlZEc=

SSV0cnVlRyUqcHJvdGVjdGVkRw==

z:=3+4*I;Re(z);Im(z);abs(z);

LCYiIiQiIiIqJiIiJUYkXiNGJEYkRiQ=

IiIk

IiIl

IiIm

solve(x^2=-1);

NiReIyIiIiwkRiMhIiI=

solve(x^5+x+1=0);

NicsJiMiIiIiIiMhIiIqJiomRiRGJV4jRiVGJUYlKSIiJEYkRiVGJSwmRiRGJyomLCRGKUYlRiVGK0YlRicsKComI0YlIiInRiUpLCYiJCsiRiUqJiIjN0YlKSIjcEYkRiVGJSNGJUYsRiVGJyomI0YmRixGJUY0RidGJ0Y7RiUsKiomI0YlRjhGJUY0RiVGJSomRjtGJUY0RidGJUY7RiUqKEYpRiVGK0YlLCZGMUYnRjxGJUYlRiUsKkY/RiVGQUYlRjtGJSooRi9GJUYrRiVGQ0YlRic=

solve(x^5+x^2+1=0);

NictSSdSb290T2ZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCwoKiQpSSNfWkdGJSIiJiIiIkYvKiQpRi0iIiNGL0YvRi9GLy9JJmluZGV4R0YlRi8tRiQ2JEYqL0Y0RjItRiQ2JEYqL0Y0IiIkLUYkNiRGKi9GNCIiJS1GJDYkRiovRjRGLg==

solve(x^7+x^6+x^5+x^4+x^3+2*x^2+x+1);

NiksJiMiIiIiIiMhIiIqJiomRiRGJV4jRiVGJUYlKSIiJEYkRiVGJSwmRiRGJyomLCRGKUYlRiVGK0YlRictSSdSb290T2ZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCwoKiQpSSNfWkdGMiIiJkYlRiUqJClGOkYmRiVGJUYlRiUvSSZpbmRleEdGMkYlLUYxNiRGNy9GP0YmLUYxNiRGNy9GP0YsLUYxNiRGNy9GPyIiJS1GMTYkRjcvRj9GOw==

evalf(%);

NiksJiQiKysrKytdISM1ISIiKiYkIitTU0RnJylGJiIiIl4jRitGK0YrLCZGJEYnRihGJywmJCIrQ0I+OnZGJkYrKiYkIis1I2ZoJXlGJkYrRixGK0YrLCYkIitubiplYSJGJkYnKiYkIitLOHUhRylGJkYrRixGK0YrJCErNiJmUT4iISIqLCZGNUYnRjdGJywmRi9GK0YxRic=

<Text-field style="Heading 3" layout="Heading 3">1.1.2. P\303\251lda.</Text-field>

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

`&+`:=(x,y)->x+y mod 2; 0&+0; 0&+1; 1&+0; 1&+1;

Zio2JEkieEc2IkkieUdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkkbW9kR0YlNiQsJkYkIiIiRiZGLiIiI0YlRiVGJQ==

IiIh

IiIi

IiIh

<Text-field style="Heading 3" layout="Heading 3">1.1.3. Algebrai strukt\303\272r\303\241k.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.1.4. P\303\251ld\303\241k.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.1.5. M\303\241trixok.</Text-field>

with(linalg);

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

a:=matrix(2,3,[x,cc,Alma,3,5]);

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

a[2,3]:=8;print(a);

IiIp

LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXJvd0dGJDYjLUknbXRhYmxlR0YkNiQtSSRtdHJHRiQ2JS1JJG10ZEdGJDYjLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GNTYjLUY4NiVRI2NjRidGO0Y+LUY1NiMtRjg2JVElQWxtYUYnRjtGPi1GMjYlLUY1NiMtSSNtbkdGJDYkUSIzRicvRj9RJ25vcm1hbEYnLUY1NiMtRlA2JFEiNUYnRlMtRjU2Iy1GUDYkUSI4RidGUy8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJw==

b:=matrix([[x,y],[9,7]]);

c:=matrix(3,2,(i,j)->i+j-1);

d:=extend(c,1,1,0);copyinto(a,d,3,2);

transpose(c);d:=transpose(%);equal(c,d);

SSV0cnVlRyUqcHJvdGVjdGVkRw==

a:=matrix(3,2);

PTYiNiQ7IiIiIiIkO0YmIiIjRVxbbCE=

entermatrix(a);

Warning, computation interrupted

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

<Text-field style="Heading 3" layout="Heading 3">1.1.6. M\305\261veletek m\303\241trixokkal.</Text-field>

a:=matrix([[1,0],[0,2]]); b:=matrix([[0,1],[0,0]]); c:=matrix([[1,0],[0,1],[0,0]]);

d:=evalm(2*a+3*b); evalm(a&*b); evalm(b&*a); evalm(sin(d)); evalm(d^2); evalm(c&*a); evalm(a&*c);

LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXJvd0dGJDYjLUknbXRhYmxlR0YkNiQtSSRtdHJHRiQ2JC1JJG10ZEdGJDYjLUkjbW5HRiQ2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GNTYjLUY4NiRRIjFGJ0Y7LUYyNiRGNEY0LyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYn

LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXJvd0dGJDYjLUknbXRhYmxlR0YkNiQtSSRtdHJHRiQ2JC1JJG10ZEdGJDYjLUkjbW5HRiQ2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GNTYjLUY4NiRRIjJGJ0Y7LUYyNiRGNEY0LyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYn

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

LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXJvd0dGJDYjLUknbXRhYmxlR0YkNiQtSSRtdHJHRiQ2JC1JJG10ZEdGJDYjLUkjbW5HRiQ2JFEiNEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GNTYjLUY4NiRRIzE4RidGOy1GMjYkLUY1NiMtRjg2JFEiMEYnRjstRjU2Iy1GODYkUSMxNkYnRjsvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRic=

LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXJvd0dGJDYjLUknbXRhYmxlR0YkNiUtSSRtdHJHRiQ2JC1JJG10ZEdGJDYjLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GNTYjLUY4NiRRIjBGJ0Y7LUYyNiRGPi1GNTYjLUY4NiRRIjJGJ0Y7LUYyNiRGPkY+LyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYn

Error, (in linalg:-multiply) non matching dimensions for vector/matrix product

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

<Text-field style="Heading 3" layout="Heading 3">1.1.7. \303\201ll\303\255t\303\241s.</Text-field>

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

<Text-field style="Heading 3" layout="Heading 3">1.1.8. Nullm\303\241trix, egys\303\251gm\303\241trix, inverz m\303\241trix.</Text-field>

a:=matrix(3,2,0); iszero(a); b:=matrix(2,2,[1,0,0,0]); iszero(b);

SSV0cnVlRyUqcHJvdGVjdGVkRw==

SSZmYWxzZUclKnByb3RlY3RlZEc=

rowdim(a); coldim(a);

IiIk

IiIj

a:=diag(3,4,5);

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

krondelta:=(i,j)-> if i=j then 1 else 0 fi;

Zio2JEkiaUc2IkkiakdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlQCUvRiRGJiIiIiIiIUYlRiVGJQ==

a:=matrix(3,3,krondelta);

b:=matrix(3,2,krondelta);

c:=hilbert(3); d:=inverse(c); evalm(c&*d); evalm(d&*c);

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjBRIzo9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJWZvcm1HUSZpbmZpeEYnLyUnbHNwYWNlR1EvdGhpY2ttYXRoc3BhY2VGJy8lJ3JzcGFjZUdGTy8lKG1pbnNpemVHUSIxRicvJShtYXhzaXplR1EpaW5maW5pdHlGJy1JKG1mZW5jZWRHRiQ2JS1GIzYjLUknbXRhYmxlR0YkNiUtSSRtdHJHRiQ2JS1JJG10ZEdGJDYjLUkjbW5HRiQ2JFEiOUYnRjktRl5vNiMtRiM2JC1GNjYwUSomdW1pbnVzMDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRJ3ByZWZpeEYnL0ZOUSQwZW1GJy9GUVEydmVyeXRoaW5tYXRoc3BhY2VGJ0ZSRlUtRmFvNiRRIzM2RidGOS1GXm82Iy1GYW82JFEjMzBGJ0Y5LUZbbzYlRmRvLUZebzYjLUZhbzYkUSQxOTJGJ0Y5LUZebzYjLUYjNiRGaG8tRmFvNiRRJDE4MEYnRjktRltvNiVGZHBGYHEtRl5vNiNGZHEvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRic=

inverse(b);

Error, (in linalg:-inverse) expecting a square matrix

a:=matrix([[2,4],[1,2]]); inverse(a);

Error, (in linalg:-inverse) singular matrix

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

<Text-field style="Heading 3" layout="Heading 3">1.1.9. Elemi sor- \303\251s oszlopm\305\261veletek.</Text-field>

a:=matrix([[1,2,3],[4,5,6]]);

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

swaprow(a,1,2);

swapcol(a,2,3);

addrow(a,1,2,-4);

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

addcol(a,2,3,-3/2);

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

<Text-field style="Heading 3" layout="Heading 3">1.1.10. Gauss-f\303\251le kik\303\274sz\303\266b\303\266l\303\251s.</Text-field>

x:='x'; y:='y'; z:='z'; eqns:={x+y/2+z/3=1,x/2+y/3+z/4=7/12,x/3+y/4+z/5=13/30};

SSJ4RzYi

SSJ5RzYi

SSJ6RzYi

PCUvLChJInhHNiIiIiIqJiNGJyIiI0YnSSJ5R0YmRidGJyomI0YnIiIkRidJInpHRiZGJ0YnRicvLCgqJkYpRidGJUYnRicqJkYtRidGK0YnRicqJiNGJyIiJUYnRi9GJ0YnIyIiKCIjNy8sKComRi1GJ0YlRidGJyomRjVGJ0YrRidGJyomI0YnIiImRidGL0YnRicjIiM4IiNJ

solve(eqns);

PCUvSSJ6RzYiIiIkL0kieEdGJSIiIi9JInlHRiUhIiM=

a:=genmatrix(eqns,[x,y,z]);

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

a:=genmatrix(eqns,[x,y,z],'b'); print(b);

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

LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUknbXRhYmxlR0YkNiMtSSRtdHJHRiQ2JS1JJG10ZEdGJDYjLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GMjYjLUkmbWZyYWNHRiQ2KC1GNTYkUSI3RidGOC1GNTYkUSMxMkYnRjgvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRksvJSliZXZlbGxlZEdRJmZhbHNlRictRjI2Iy1GPjYoLUY1NiRRIzEzRidGOC1GNTYkUSMzMEYnRjhGRkZJRkxGTi8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJw==

geneqns(a,[x,y,z],b);

c:=augment(a,b);

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

genmatrix(eqns,[x,y,z],flag);

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

<Text-field style="Heading 3" layout="Heading 3">1.1.11. P\303\251ld\303\241k.</Text-field>

c1:=pivot(c,1,1,2..3);

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

c2:=pivot(c1,2,2,3..3);

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

gausselim(c,3);

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

backsub(c2);

LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUknbXRhYmxlR0YkNiMtSSRtdHJHRiQ2JS1JJG10ZEdGJDYjLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GMjYjLUklbXJvd0dGJDYkLUkjbW9HRiQ2MFEqJnVtaW51czA7RidGOC8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRi8lKXN0cmV0Y2h5R0ZGLyUqc3ltbWV0cmljR0ZGLyUobGFyZ2VvcEdGRi8lLm1vdmFibGVsaW1pdHNHRkYvJSdhY2NlbnRHRkYvJSVmb3JtR1EncHJlZml4RicvJSdsc3BhY2VHUSQwZW1GJy8lJ3JzcGFjZUdRMnZlcnl0aGlubWF0aHNwYWNlRicvJShtaW5zaXplR0Y3LyUobWF4c2l6ZUdRKWluZmluaXR5RictRjU2JFEiMkYnRjgtRjI2Iy1GNTYkUSIzRidGOC8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJw==

d:=copy(c); d[3,3]:=7/36; print(d);

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

IyIiKCIjTw==

LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXJvd0dGJDYjLUknbXRhYmxlR0YkNiUtSSRtdHJHRiQ2Ji1JJG10ZEdGJDYjLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GNTYjLUkmbWZyYWNHRiQ2KEY3LUY4NiRRIjJGJ0Y7LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZLLyUpYmV2ZWxsZWRHUSZmYWxzZUYnLUY1NiMtRkE2KEY3LUY4NiRRIjNGJ0Y7RkZGSUZMRk5GNC1GMjYmRj5GUS1GNTYjLUZBNihGNy1GODYkUSI0RidGO0ZGRklGTEZOLUY1NiMtRkE2KC1GODYkUSI3RidGOy1GODYkUSMxMkYnRjtGRkZJRkxGTi1GMjYmRlFGWi1GNTYjLUZBNihGX28tRjg2JFEjMzZGJ0Y7RkZGSUZMRk4tRjU2Iy1GQTYoLUY4NiRRIzEzRidGOy1GODYkUSMzMEYnRjtGRkZJRkxGTi8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJw==

d1:=pivot(d,1,1,2..3);

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

d2:=pivot(d1,2,2,3..3);

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

backsub(d2);

Error, (in linalg:-backsub) inconsistent system

e:=copy(d); e[3,4]:=5/12; print(e);

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

IyIiJiIjNw==

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

e1:=pivot(e,1,1,2..3);

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEjZTFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYwUSM6PUYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSVmb3JtR1EmaW5maXhGJy8lJ2xzcGFjZUdRL3RoaWNrbWF0aHNwYWNlRicvJSdyc3BhY2VHRk8vJShtaW5zaXplR1EiMUYnLyUobWF4c2l6ZUdRKWluZmluaXR5RictSShtZmVuY2VkR0YkNiUtRiM2Iy1JJ210YWJsZUdGJDYlLUkkbXRyR0YkNiYtSSRtdGRHRiQ2Iy1JI21uR0YkNiRGVEY5LUZebzYjLUkmbWZyYWNHRiQ2KEZgby1GYW82JFEiMkYnRjkvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmBwLyUpYmV2ZWxsZWRHRj0tRl5vNiMtRmZvNihGYG8tRmFvNiRRIjNGJ0Y5RltwRl5wRmFwRmNwRl1vLUZbbzYmLUZebzYjLUZhbzYkUSIwRidGOS1GXm82Iy1GZm82KEZgby1GYW82JFEjMTJGJ0Y5RltwRl5wRmFwRmNwRmNxRmNxRlxxLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYn

e2:=pivot(e1,2,2,3..3);

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

backsub(e2);

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

evalm(randmatrix(3,4)+I*randmatrix(3,4)); gausselim(%); backsub(%);

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

<Text-field style="Heading 3" layout="Heading 3">1.1.12. M\303\263dos\303\255tott Gauss-f\303\251le kik\303\274sz\303\266b\303\266l\303\251s.</Text-field>

print(c);

c1:=pivot(c,1,1,2..3);

mulrow(c1,2,12); c2:=pivot(%,2,2,3..3);

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

c3:=mulrow(c2,3,180);

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

backsub(c3);

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

<Text-field style="Heading 3" layout="Heading 3">1.1.13. M\303\241trixinverzi\303\263 Gauss-f\303\251le kik\303\274sz\303\266b\303\266l\303\251ssel.</Text-field>

a:=hilbert(3); b:=diag(1,1,1); c:=augment(a,b);

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

cc:=gausselim(c,3);

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

aa:=submatrix(cc,1..3,1..3); bb:=submatrix(cc,1..3,4..6);

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

backsub(aa,bb); inverse(a);

LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXJvd0dGJDYjLUknbXRhYmxlR0YkNiUtSSRtdHJHRiQ2JS1JJG10ZEdGJDYjLUkjbW5HRiQ2JFEiOUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GNTYjLUYsNiQtSSNtb0dGJDYwUSomdW1pbnVzMDtGJ0Y7LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZILyUpc3RyZXRjaHlHRkgvJSpzeW1tZXRyaWNHRkgvJShsYXJnZW9wR0ZILyUubW92YWJsZWxpbWl0c0dGSC8lJ2FjY2VudEdGSC8lJWZvcm1HUSdwcmVmaXhGJy8lJ2xzcGFjZUdRJDBlbUYnLyUncnNwYWNlR1EydmVyeXRoaW5tYXRoc3BhY2VGJy8lKG1pbnNpemVHUSIxRicvJShtYXhzaXplR1EpaW5maW5pdHlGJy1GODYkUSMzNkYnRjstRjU2Iy1GODYkUSMzMEYnRjstRjI2JUY+LUY1NiMtRjg2JFEkMTkyRidGOy1GNTYjLUYsNiRGQi1GODYkUSQxODBGJ0Y7LUYyNiVGYW9GXXAtRjU2I0ZhcC8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJw==

linsolve(a,b);

<Text-field style="Heading 3" layout="Heading 3">1.1.14. Gauss-Jordan kik\303\274sz\303\266b\303\266l\303\251s.</Text-field>

print(c);

c1:=pivot(c,1,1);

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

mulrow(c1,2,12); c2:=pivot(%,2,2);

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

mulrow(c2,3,180); c3:=pivot(%,3,3);

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

gaussjord(c,3);

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

<Text-field style="Heading 3" layout="Heading 3">*1.1.15. A m\305\261veletig\303\251nyek \303\266sszehasonl\303\255t\303\241sa.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">*1.1.16. A h\303\241romsz\303\266gm\303\241trixok m\303\263dszere.</Text-field>

u:=LUdecomp(a,P='p',L='l');

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

print(p); print(l); evalm(p&*l&*u);

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

forwardsub(l,b); backsub(u,%);

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

<Text-field style="Heading 3" layout="Heading 3">*1.1.17. Numerikus megjegyz\303\251sek.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.1.18. Vektort\303\251r.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.1.19. P\303\251ld\303\241k.</Text-field>

v:=vector(3,[5,6]);

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

v[3]:=7; print(v);

IiIo

LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUknbXRhYmxlR0YkNiMtSSRtdHJHRiQ2JS1JJG10ZEdGJDYjLUkjbW5HRiQ2JFEiNUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GMjYjLUY1NiRRIjZGJ0Y4LUYyNiMtRjU2JFEiN0YnRjgvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRic=

u:=vector(3,i->i+1);

evalm(2*u+v);

LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUknbXRhYmxlR0YkNiMtSSRtdHJHRiQ2JS1JJG10ZEdGJDYjLUkjbW5HRiQ2JFEiOUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GMjYjLUY1NiRRIzEyRidGOC1GMjYjLUY1NiRRIzE1RidGOC8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJw==

w:=vector(4,0); vectdim(w);

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

IiIl

w:=randvector(3);

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

type(w,'vector'); type(w,'matrix');

SSV0cnVlRyUqcHJvdGVjdGVkRw==

SSZmYWxzZUclKnByb3RlY3RlZEc=

<Text-field style="Heading 3" layout="Heading 3">1.1.20 Alt\303\251r.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.1.21. P\303\251ld\303\241k.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.1.22. Line\303\241ris kombin\303\241ci\303\263.</Text-field>

evalm(-87*z-7/3*u+16/3*v);

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

<Text-field style="Heading 3" layout="Heading 3">1.1.23. Megjegyz\303\251s.</Text-field>

z:=vector([1,0,0]); a:=augment(z,u,v,w);

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

b:=stackmatrix(u,v,w,z);

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

col(a,2);

LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUknbXRhYmxlR0YkNiMtSSRtdHJHRiQ2JS1JJG10ZEdGJDYjLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GMjYjLUY1NiRRIjNGJ0Y4LUYyNiMtRjU2JFEiNEYnRjgvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRic=

col(a,2..3);

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYlLUknbXRhYmxlR0YkNiMtSSRtdHJHRiQ2JS1JJG10ZEdGJDYjLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GNTYjLUY4NiRRIjNGJ0Y7LUY1NiMtRjg2JFEiNEYnRjsvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRictSSNtb0dGJDYwUSIsRidGOy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0ZULyUqc3ltbWV0cmljR0ZULyUobGFyZ2VvcEdGVC8lLm1vdmFibGVsaW1pdHNHRlQvJSdhY2NlbnRHRlQvJSVmb3JtR1EmaW5maXhGJy8lJ2xzcGFjZUdRJDBlbUYnLyUncnNwYWNlR1EzdmVyeXRoaWNrbWF0aHNwYWNlRicvJShtaW5zaXplR1EiMUYnLyUobWF4c2l6ZUdRKWluZmluaXR5RictRiw2JS1GLzYjLUYyNiUtRjU2Iy1GODYkUSI1RidGOy1GNTYjLUY4NiRRIjZGJ0Y7LUY1NiMtRjg2JFEiN0YnRjtGSEZL

row(a,2);

LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUknbXRhYmxlR0YkNiMtSSRtdHJHRiQ2Ji1JJG10ZEdGJDYjLUkjbW5HRiQ2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GMjYjLUY1NiRRIjNGJ0Y4LUYyNiMtRjU2JFEiNkYnRjgtRjI2Iy1GNTYkUSM3NUYnRjgvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRic=

row(a,2..3);

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

subvector(b,3,2..3); subvector(b,1..3,2);

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

LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUknbXRhYmxlR0YkNiMtSSRtdHJHRiQ2JS1JJG10ZEdGJDYjLUkjbW5HRiQ2JFEiM0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GMjYjLUY1NiRRIjZGJ0Y4LUYyNiMtRjU2JFEjNzVGJ0Y4LyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYn

<Text-field style="Heading 3" layout="Heading 3">1.1.24. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">*1.1.25. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.1.26. Gener\303\241torrendszer, dimenzi\303\263.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.1.27. Line\303\241ris f\303\274ggetlens\303\251g \303\251s f\303\274gg\305\221s\303\251g.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.1.28. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.1.29. B\303\241zis.</Text-field>

basis([z,u,v,w]); basis([u,v,w,z]);

NyVJInpHNiJJInVHRiRJInZHRiQ=

NyVJInVHNiJJInZHRiRJIndHRiQ=

intbasis([z,u],[u,v,w]); intbasis([z,u],[v,w]); intbasis([z,u],[v]);

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

LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXJvd0dGJDYjLUYjNiUtSSdtdGFibGVHRiQ2Iy1JJG10ckdGJDYlLUkkbXRkR0YkNiMtRiw2JC1JI21vR0YkNjBRKiZ1bWludXMwO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSVmb3JtR1EncHJlZml4RicvJSdsc3BhY2VHUSQwZW1GJy8lJ3JzcGFjZUdRMnZlcnl0aGlubWF0aHNwYWNlRicvJShtaW5zaXplR1EiMUYnLyUobWF4c2l6ZUdRKWluZmluaXR5RictSSNtbkdGJDYkUSQ5MzdGJ0Y/LUY3NiMtRiw2JEY7LUZbbzYkUSUxMDc3RidGPy1GNzYjLUYsNiRGOy1GW282JFElMTQzNkYnRj8vJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRicvRl1wUSJ8ZnJGJy9GYHBRInxockYn

PCI=

sumbasis([z,u],[v,w]);

NyVJInpHNiJJInVHRiRJInZHRiQ=

<Text-field style="Heading 3" layout="Heading 3">1.1.30. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.1.31. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.1.32. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.1.33. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.1.34. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.1.35. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.1.36. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.1.37. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.1.38. Rang.</Text-field>

basis(a,colspace); basis(a,rowspace);

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

print(a); backsub(gausselim(a));

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

<Text-field style="Heading 3" layout="Heading 3">1.1.39. Megjegyz\303\251s.</Text-field>

rank(a); gausselim(a,'ra');ra;

IiIk

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

IiIk

rank(b); gausselim(b,'rb');rb;

IiIk

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

IiIk

<Text-field style="Heading 3" layout="Heading 3">1.1.40. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.1.41. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.1.42. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.1.43. Koordin\303\241t\303\241k.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.1.44. Izomorfia.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.1.45. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">*1.1.46. Vektorterek direkt \303\266sszege.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">*1.1.48. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">*1.1.49. P\303\251lda.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.1.50. Affin sokas\303\241gok.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.1.51. T\303\251tel.</Text-field>

x:=vector([1+t,2-t,t-1]); x0:=map2(subs,t=0,x); y:=evalm(x-x0);

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

y1:=map2(subs,t=1,y);

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

z:=evalm(x0+t*y1);

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjBRIzo9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJWZvcm1HUSZpbmZpeEYnLyUnbHNwYWNlR1EvdGhpY2ttYXRoc3BhY2VGJy8lJ3JzcGFjZUdGTy8lKG1pbnNpemVHUSIxRicvJShtYXhzaXplR1EpaW5maW5pdHlGJy1JKG1mZW5jZWRHRiQ2JS1JJ210YWJsZUdGJDYjLUkkbXRyR0YkNiUtSSRtdGRHRiQ2Iy1GIzYlLUkjbW5HRiQ2JEZURjktRjY2MFEiK0YnRjlGO0Y+RkBGQkZERkZGSEZKL0ZOUTBtZWRpdW1tYXRoc3BhY2VGJy9GUUZnb0ZSRlUtRiw2JVEidEYnRi9GMi1GXG82Iy1GIzYlLUZhbzYkUSIyRidGOS1GNjYwUSgmbWludXM7RidGOUY7Rj5GQEZCRkRGRkZIRkpGZm9GaG9GUkZVRmlvLUZcbzYjLUYjNiVGaW9GY3BGYG8vJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRic=

<Text-field style="Heading 3" layout="Heading 3">1.1.52. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.1.53. K\303\266vetkezm\303\251ny.</Text-field>

x:=vector([1+t1,2-t2,t1+t2-1]); x0=map2(subs,[t1=0,t2=0],x); y:=evalm(x-x0);

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjBRIzo9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJWZvcm1HUSZpbmZpeEYnLyUnbHNwYWNlR1EvdGhpY2ttYXRoc3BhY2VGJy8lJ3JzcGFjZUdGTy8lKG1pbnNpemVHUSIxRicvJShtYXhzaXplR1EpaW5maW5pdHlGJy1JKG1mZW5jZWRHRiQ2JS1JJ210YWJsZUdGJDYjLUkkbXRyR0YkNiUtSSRtdGRHRiQ2Iy1GLDYlUSN0MUYnRi9GMi1GXG82Iy1GIzYkLUY2NjBRKiZ1bWludXMwO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EncHJlZml4RicvRk5RJDBlbUYnL0ZRUTJ2ZXJ5dGhpbm1hdGhzcGFjZUYnRlJGVS1GLDYlUSN0MkYnRi9GMi1GXG82Iy1GIzYlRl5vLUY2NjBRIitGJ0Y5RjtGPkZARkJGREZGRkhGSi9GTlEwbWVkaXVtbWF0aHNwYWNlRicvRlFGaXBGUkZVRl5wLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYn

y1:=map2(subs,[t1=1,t2=0],y); y2:=map2(subs,[t1=0,t2=1],y);

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

z:=evalm(x0+t1*y1+t2*y2);

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

x:=vector([1+t1+t3,2+t2+t3,-1,2]); x0:=map2(subs,[t1=0,t2=0,t3=0],x); y:=evalm(x-x0);

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEjeDBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYwUSM6PUYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSVmb3JtR1EmaW5maXhGJy8lJ2xzcGFjZUdRL3RoaWNrbWF0aHNwYWNlRicvJSdyc3BhY2VHRk8vJShtaW5zaXplR1EiMUYnLyUobWF4c2l6ZUdRKWluZmluaXR5RictSShtZmVuY2VkR0YkNiUtSSdtdGFibGVHRiQ2Iy1JJG10ckdGJDYmLUkkbXRkR0YkNiMtSSNtbkdGJDYkRlRGOS1GXG82Iy1GX282JFEiMkYnRjktRlxvNiMtRiM2JC1GNjYwUSomdW1pbnVzMDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRJ3ByZWZpeEYnL0ZOUSQwZW1GJy9GUVEydmVyeXRoaW5tYXRoc3BhY2VGJ0ZSRlVGXm9GYW8vJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRic=

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

y1:=map2(subs,[t1=1,t2=0,t3=0],y); y2:=map2(subs,[t1=0,t2=1,t3=0],y); y3:=map2(subs,[t1=0,t2=0,t3=1],y);

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

basis([y1,y2,y3]);

NyRJI3kxRzYiSSN5MkdGJA==

z:=evalm(x0+u1*y1+u2*y2);

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

<Text-field style="Heading 3" layout="Heading 3">1.1.54. Affin sokas\303\241g dimenzi\303\263ja.</Text-field>

<Text-field style="Heading 2" layout="Heading 2">1.2. Line\303\241ris lek\303\251pez\303\251sek</Text-field>

restart;with(linalg);

N15ySS5CbG9ja0RpYWdvbmFsRzYiSSxHcmFtU2NobWlkdEdGJEksSm9yZGFuQmxvY2tHRiRJKUxVZGVjb21wR0YkSSlRUmRlY29tcEdGJEkqV3JvbnNraWFuR0YkSSdhZGRjb2xHRiRJJ2FkZHJvd0dGJEkkYWRqR0YkSShhZGpvaW50R0YkSSZhbmdsZUdGJEkoYXVnbWVudEdGJEkoYmFja3N1YkdGJEklYmFuZEdGJEkmYmFzaXNHRiRJJ2Jlem91dEdGJEksYmxvY2ttYXRyaXhHRiRJKGNoYXJtYXRHRiRJKWNoYXJwb2x5R0YkSSljaG9sZXNreUdGJEkkY29sR0YkSSdjb2xkaW1HRiRJKWNvbHNwYWNlR0YkSShjb2xzcGFuR0YkSSpjb21wYW5pb25HRiRJJ2NvbmNhdEdGJEklY29uZEdGJEkpY29weWludG9HRiRJKmNyb3NzcHJvZEdGJEklY3VybEdGJEkpZGVmaW5pdGVHRiRJKGRlbGNvbHNHRiRJKGRlbHJvd3NHRiRJJGRldEdGJEklZGlhZ0dGJEkoZGl2ZXJnZUdGJEkoZG90cHJvZEdGJEkqZWlnZW52YWxzR0YkSSxlaWdlbnZhbHVlc0dGJEktZWlnZW52ZWN0b3JzR0YkSStlaWdlbnZlY3RzR0YkSSxlbnRlcm1hdHJpeEdGJEkmZXF1YWxHRiRJLGV4cG9uZW50aWFsR0YkSSdleHRlbmRHRiRJLGZmZ2F1c3NlbGltR0YkSSpmaWJvbmFjY2lHRiRJK2ZvcndhcmRzdWJHRiRJKmZyb2Jlbml1c0dGJEkqZ2F1c3NlbGltR0YkSSpnYXVzc2pvcmRHRiRJKGdlbmVxbnNHRiRJKmdlbm1hdHJpeEdGJEklZ3JhZEdGJEkpaGFkYW1hcmRHRiRJKGhlcm1pdGVHRiRJKGhlc3NpYW5HRiRJKGhpbGJlcnRHRiRJK2h0cmFuc3Bvc2VHRiRJKWloZXJtaXRlR0YkSSppbmRleGZ1bmNHRiRJKmlubmVycHJvZEdGJEkpaW50YmFzaXNHRiRJKGludmVyc2VHRiRJJ2lzbWl0aEdGJEkqaXNzaW1pbGFyR0YkSSdpc3plcm9HRiRJKWphY29iaWFuR0YkSSdqb3JkYW5HRiRJJ2tlcm5lbEdGJEkqbGFwbGFjaWFuR0YkSSpsZWFzdHNxcnNHRiRJKWxpbnNvbHZlR0YkSSdtYXRhZGRHRiRJJ21hdHJpeEdGJEkmbWlub3JHRiRJKG1pbnBvbHlHRiRJJ211bGNvbEdGJEknbXVscm93R0YkSSltdWx0aXBseUdGJEklbm9ybUdGJEkqbm9ybWFsaXplR0YkSSpudWxsc3BhY2VHRiRJJ29ydGhvZ0dGJEkqcGVybWFuZW50R0YkSSZwaXZvdEdGJEkqcG90ZW50aWFsR0YkSStyYW5kbWF0cml4R0YkSStyYW5kdmVjdG9yR0YkSSVyYW5rR0YkSShyYXRmb3JtR0YkSSRyb3dHRiRJJ3Jvd2RpbUdGJEkpcm93c3BhY2VHRiRJKHJvd3NwYW5HRiRJJXJyZWZHRiRJKnNjYWxhcm11bEdGJEktc2luZ3VsYXJ2YWxzR0YkSSZzbWl0aEdGJEksc3RhY2ttYXRyaXhHRiRJKnN1Ym1hdHJpeEdGJEkqc3VidmVjdG9yR0YkSSlzdW1iYXNpc0dGJEkoc3dhcGNvbEdGJEkoc3dhcHJvd0dGJEkqc3lsdmVzdGVyR0YkSSl0b2VwbGl0ekdGJEkmdHJhY2VHRiRJKnRyYW5zcG9zZUdGJEksdmFuZGVybW9uZGVHRiRJKnZlY3BvdGVudEdGJEkodmVjdGRpbUdGJEkndmVjdG9yR0YkSSp3cm9uc2tpYW5HRiQ=

<Text-field style="Heading 3" layout="Heading 3">1.2.1. Line\303\241ris lek\303\251pez\303\251sek.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.2. P\303\251ld\303\241k line\303\241ris lek\303\251pez\303\251sekre.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.3. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.4. Line\303\241ris lek\303\251pez\303\251sek \303\266sszege \303\251s skal\303\241rszorosa.</Text-field>

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

<Text-field style="Heading 3" layout="Heading 3">1.2.5. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.6. Line\303\241ris lek\303\251pez\303\251sek szorzata.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.7. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.8. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.9. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.10. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.11. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.12. Vektorrendszer \303\251s lek\303\251pez\303\251s m\303\241trixa.</Text-field>

a:=matrix([[1,1,2,5,0],[0,1,1,3,-1],[1,0,1,2,1]]);

PTYiNiQ7IiIiIiIkO0YmIiImRVxbbDA2JEYnRidGJjYkIiIjRiYiIiE2JEYnRi1GLjYkRi1GLUYmNiRGLUYnRiY2JEYnRiZGJjYkRi0iIiVGJzYkRi1GKSEiIjYkRiZGJ0YtNiRGJkYmRiY2JEYmRi1GJjYkRiZGKUYuNiRGJ0Y0Ri02JEYmRjRGKTYkRidGKUYm

colspace(a); rank(a); kernel(a); coldim(a);

PCQ9NiI2IzsiIiIiIiRFXFtsJEYnRiciIiMiIiFGKEYnPUYkRiVFXFtsJEYnRitGKkYnRighIiI=

IiIj

PCU9NiI2IzsiIiIiIiZFXFtsJkYnISIiIiIjRioiIiRGJ0YoIiIhIiIlRi09RiRGJUVcW2wmRichIiNGKyEiJEYsRi1GKEYtRi5GJz1GJEYlRVxbbCZGJ0YqRitGJ0YsRi1GKEYnRi5GLQ==

IiIm

<Text-field style="Heading 3" layout="Heading 3">1.2.13. T\303\251tel.</Text-field>

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

a:=matrix([[1,2,3],[2,3,4],[3,4,5]]); x:=vector([1,0,1]); multiply(a,x);

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyIiJjYkIiIjRiZGLDYkRidGLCIiJTYkRixGLEYnNiRGLEYnRi42JEYnRiZGJzYkRiZGJ0YnNiRGJkYmRiY2JEYmRixGLA==

PTYiNiM7IiIiIiIkRVxbbCRGJkYmIiIjIiIhRidGJg==

PTYiNiM7IiIiIiIkRVxbbCRGJiIiJSIiIyIiJ0YnIiIp

<Text-field style="Heading 3" layout="Heading 3">1.2.14. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.15. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.16. \303\201tt\303\251r\303\251sm\303\241trix.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.17. P\303\251ld\303\241k: egyszer\305\261 b\303\241zistranszform\303\241ci\303\263k.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.18. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.19. K\303\266vetkezm\303\251ny.</Text-field>

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

<Text-field style="Heading 3" layout="Heading 3">1.2.20. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.21. Ekvivalens transzform\303\241ci\303\263k, ekvivalens m\303\241trixok.</Text-field>

t:=matrix([[1,1,0],[0,1,1],[1,0,1]]); rank(t);

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJ0YmNiQiIiNGJiIiITYkRidGK0YsNiRGK0YrRiY2JEYrRidGJjYkRidGJkYmNiRGJkYnRiw2JEYmRiZGJjYkRiZGK0Ym

IiIk

b:=evalm(inverse(t)&*a&*t);

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyMiIzYiIiM2JEYsRiZGJjYkRidGLCMiIipGLDYkRixGLCNGJkYsNiRGLEYnI0YnRiw2JEYnRiYiIiY2JEYmRicjIiIoRiw2JEYmRiZGJzYkRiZGLCNGNkYs

s:=matrix([[1,-2,0],[0,1,-2],[-2,0,1]]); rank(s);

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJ0YmNiQiIiNGJiIiITYkRidGK0YsNiRGK0YrRiY2JEYrRichIiM2JEYnRiZGMDYkRiZGJ0YsNiRGJkYmRiY2JEYmRitGMA==

IiIk

evalm(inverse(s)&*evalm(a&*t));

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyMhI1oiIig2JCIiI0YmIyEjUUYsNiRGJ0YuIyEjTEYsNiRGLkYuIyEjSkYsNiRGLkYnIyEjWEYsNiRGJ0YmIyEjU0YsNiRGJkYnIyEjYkYsNiRGJkYmIyEjW0YsNiRGJkYuIyEjVEYs

augment(s,evalm(a&*t)); gaussjord(%,3);

PTYiNiQ7IiIiIiIkO0YmIiInRVxbbDM2JEYnRidGJjYkIiIjRiYiIiE2JEYnRi1GLjYkRi1GLUYmNiRGLUYnISIjNiRGJ0YmRjI2JEYtIiIlRik2JEYmRikiIiY2JEYtRjdGNzYkRiZGJ0YuNiRGJkYmRiY2JEYmRi1GMjYkRiZGN0YnNiRGJ0Y1IiIpNiRGJ0YpIiIqNiRGLUYpIiIoNiRGJkY1RjU2JEYnRjdGQg==

PTYiNiQ7IiIiIiIkO0YmIiInRVxbbDM2JEYnRidGJjYkIiIjRiYiIiE2JEYnRi1GLjYkRi1GLUYmNiRGLUYnRi42JEYnRiZGLjYkRi0iIiUjISNRIiIoNiRGJkYpIyEjYkY3NiRGLSIiJiMhI0pGNzYkRiZGJ0YuNiRGJkYmRiY2JEYmRi1GLjYkRiZGPCMhI1RGNzYkRidGNCMhI1NGNzYkRidGKSMhI1pGNzYkRi1GKSMhI1hGNzYkRiZGNCMhI1tGNzYkRidGPCMhI0xGNw==

<Text-field style="Heading 3" layout="Heading 3">1.2.22. Line\303\241ris form\303\241k.</Text-field>

f:=matrix(1,4); x:=vector(4); multiply(f,x);

PTYiNiQ7IiIiRiY7RiYiIiVFXFtsIQ==

PTYiNiM7IiIiIiIlRVxbbCE=

PTYiNiM7IiIiRiZFXFtsIkYmLCoqJiZJImZHRiM2JEYmRiZGJiZJInhHRiM2I0YmRiZGJiomJkYrNiRGJiIiI0YmJkYuNiNGM0YmRiYqJiZGKzYkRiYiIiRGJiZGLjYjRjlGJkYmKiYmRis2JEYmIiIlRiYmRi42I0Y/RiZGJg==

<Text-field style="Heading 3" layout="Heading 3">*1.2.23. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.24. Biline\303\241ris lek\303\251pez\303\251sek.</Text-field>

a:=matrix(2,3); x:=vector(2); y:=vector(3); innerprod(x,a,y); evalm(x&*a&*y);

PTYiNiQ7IiIiIiIjO0YmIiIkRVxbbCE=

PTYiNiM7IiIiIiIjRVxbbCE=

PTYiNiM7IiIiIiIkRVxbbCE=

LC4qKCZJInlHNiI2IyIiIkYoJkkieEdGJkYnRigmSSJhR0YmNiRGKEYoRihGKCooRiRGKCZGKjYjIiIjRigmRiw2JEYxRihGKEYoKigmRiVGMEYoRilGKCZGLDYkRihGMUYoRigqKEY1RihGL0YoJkYsNiRGMUYxRihGKCooJkYlNiMiIiRGKEYpRigmRiw2JEYoRj5GKEYoKihGPEYoRi9GKCZGLDYkRjFGPkYoRig=

LCgqJiwmKiYmSSJ4RzYiNiMiIiJGKiZJImFHRig2JEYqRipGKkYqKiYmRic2IyIiI0YqJkYsNiRGMUYqRipGKkYqJkkieUdGKEYpRipGKiomLCYqJkYmRiomRiw2JEYqRjFGKkYqKiZGL0YqJkYsNiRGMUYxRipGKkYqJkY1RjBGKkYqKiYsJiomRiZGKiZGLDYkRioiIiRGKkYqKiZGL0YqJkYsNiRGMUZERipGKkYqJkY1NiNGREYqRio=

x:=vector(3); innerprod(x,y);

PTYiNiM7IiIiIiIkRVxbbCE=

LCgqJiZJInhHNiI2IyIiIkYoJkkieUdGJkYnRihGKComJkYlNiMiIiNGKCZGKkYtRihGKComJkYlNiMiIiRGKCZGKkYyRihGKA==

<Text-field style="Heading 3" layout="Heading 3">1.2.25. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.26. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.27. Kvadratikus lek\303\251pez\303\251sek.</Text-field>

b:=matrix([[1,2,3],[2,3,4],[5,6,7]]); q:=innerprod(x,b,x);

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyIiKDYkIiIjRiZGLDYkRidGLCIiJzYkRixGLEYnNiRGLEYnIiIlNiRGJ0YmIiImNiRGJkYnRic2JEYmRiZGJjYkRiZGLEYs

LC4qJCkmSSJ4RzYiNiMiIiIiIiNGKUYpKigiIiVGKUYlRikmRiY2I0YqRilGKSooIiIpRilGJUYpJkYmNiMiIiRGKUYpKiZGM0YpKUYtRipGKUYpKigiIzVGKUYtRilGMUYpRikqJiIiKEYpKUYxRipGKUYp

<Text-field style="Heading 3" layout="Heading 3">1.2.28. T\303\251tel.</Text-field>

s:=evalm(1/2*b+1/2*transpose(b)); a:=evalm(1/2*b-1/2*transpose(b));

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyIiKDYkIiIjRiZGLDYkRidGLCIiJjYkRixGLEYnNiRGLEYnRi42JEYnRiYiIiU2JEYmRidGMjYkRiZGJkYmNiRGJkYsRiw=

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyIiITYkIiIjRiZGKjYkRidGLEYmNiRGLEYsRio2JEYsRichIiI2JEYnRiZGJjYkRiZGJ0YwNiRGJkYmRio2JEYmRixGKg==

innerprod(x,s,x); innerprod(x,a,x);

LC4qJCkmSSJ4RzYiNiMiIiIiIiNGKUYpKigiIiVGKUYlRikmRiY2I0YqRilGKSooIiIpRilGJUYpJkYmNiMiIiRGKUYpKiZGM0YpKUYtRipGKUYpKigiIzVGKUYtRilGMUYpRikqJiIiKEYpKUYxRipGKUYp

IiIh

<Text-field style="Heading 3" layout="Heading 3">1.2.29. P\303\251lda: vektori szorzat.</Text-field>

a:=matrix([[0,k,-j],[-k,0,i],[j,-i,0]]); b:=innerprod(x,a,y);

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyIiITYkIiIjRiYsJEkia0dGIyEiIjYkRidGLCwkSSJpR0YjRi82JEYsRixGKjYkRixGJ0YyNiRGJ0YmSSJqR0YjNiRGJkYnLCRGNkYvNiRGJkYmRio2JEYmRixGLg==

LC4qKCZJInlHNiI2IyIiIkYoJkkieEdGJjYjIiIjRihJImtHRiZGKCEiIiooRiRGKCZGKjYjIiIkRihJImpHRiZGKEYoKigmRiVGK0YoJkYqRidGKEYtRihGKCooRjVGKEYwRihJImlHRiZGKEYuKigmRiVGMUYoRjZGKEYzRihGLiooRjpGKEYpRihGOEYoRig=

i:=vector([1,0,0]); j:=vector([0,1,0]); k:=vector([0,0,1]); evalm(b);

PTYiNiM7IiIiIiIkRVxbbCRGJkYmIiIjIiIhRidGKg==

PTYiNiM7IiIiIiIkRVxbbCRGJiIiISIiI0YmRidGKQ==

PTYiNiM7IiIiIiIkRVxbbCRGJiIiISIiI0YpRidGJg==

PTYiNiM7IiIiIiIkRVxbbCRGJiwmKiYmSSJ5R0YjNiMiIiNGJiZJInhHRiM2I0YnRiYhIiIqJiZGLEYxRiYmRjBGLUYmRiZGLiwmKiYmRiw2I0YmRiZGL0YmRiYqJkY0RiYmRjBGOUYmRjJGJywmKiZGOEYmRjVGJkYyKiZGK0YmRjtGJkYm

crossprod(x,y);

PTYiNiM7IiIiIiIkRVxbbCRGJiwmKiYmSSJ5R0YjNiMiIiNGJiZJInhHRiM2I0YnRiYhIiIqJiZGLEYxRiYmRjBGLUYmRiZGLiwmKiYmRiw2I0YmRiZGL0YmRiYqJkY0RiYmRjBGOUYmRjJGJywmKiZGOEYmRjVGJkYyKiZGK0YmRjtGJkYm

<Text-field style="Heading 3" layout="Heading 3">1.2.30. T\303\251tel: szimmetrikus \303\251s altern\303\241l\303\263 biline\303\241ris lek\303\251pez\303\251sek m\303\241trixa.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.31. Szimmetrikus biline\303\241ris form\303\241k \303\241tl\303\263s alakra hoz\303\241sa.</Text-field>

print(s); addcol(s,1,2,-2); addrow(%,1,2,-2); addcol(%,1,3,-4); s1:=addrow(%,1,3,-4);

SSJzRzYi

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyIiKDYkIiIjRiZGLDYkRidGLCEiJDYkRixGLCEiIjYkRixGJyIiJjYkRidGJiIiJTYkRiZGJ0Y0NiRGJkYmRiY2JEYmRiwiIiE=

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyIiKDYkIiIjRiYiIiE2JEYnRiwhIiQ2JEYsRiwhIiI2JEYsRidGLzYkRidGJiIiJTYkRiZGJ0Y0NiRGJkYmRiY2JEYmRixGLQ==

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyEiKjYkIiIjRiYiIiE2JEYnRiwhIiQ2JEYsRiwhIiI2JEYsRidGLzYkRidGJiIiJTYkRiZGJ0YtNiRGJkYmRiY2JEYmRixGLQ==

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyEiKjYkIiIjRiYiIiE2JEYnRiwhIiQ2JEYsRiwhIiI2JEYsRidGLzYkRidGJkYtNiRGJkYnRi02JEYmRiZGJjYkRiZGLEYt

addcol(s1,2,3,-3); s2:=addrow(%,2,3,-3);

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyIiITYkIiIjRiZGKjYkRidGLCEiJDYkRixGLCEiIjYkRixGJ0YqNiRGJ0YmRio2JEYmRidGKjYkRiZGJkYmNiRGJkYsRio=

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyIiITYkIiIjRiZGKjYkRidGLEYqNiRGLEYsISIiNiRGLEYnRio2JEYnRiZGKjYkRiZGJ0YqNiRGJkYmRiY2JEYmRixGKg==

<Text-field style="Heading 3" layout="Heading 3">1.2.32. Megjegyz\303\251s.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">*1.2.33. Antiszimmetrikus biline\303\241ris form\303\241k \303\241tl\303\263s alakra hoz\303\241sa. </Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.34. Definit \303\251s indefinit kvadratikus form\303\241k.</Text-field>

definite(s,'positive_def'); definite(s,'positive_semidef'); definite(s,'negative_semidef');

SSZmYWxzZUclKnByb3RlY3RlZEc=

princaxis:=proc(b) local a,i,j,k,n,x; if not(type(b,'matrix'(rational,square)) or type(b,'matrix'(float,square))) then ERROR(`Invalid argument`) fi; n:=coldim(b); for i to n do for j from i+1 to n do if b[i,j]<>b[j,i] then ERROR(`Invalid argument`) fi; od; od; a:=copy(b); for k to n do if a[k,k]=0 then for j from k+1 to n do if a[j,j]<>0 then break fi; od; if j<=n then a:=swapcol(a,k,j); a:=swaprow(a,k,j); fi; fi; if a[k,k]=0 then for j from k+1 to n do if a[k,j]<>0 then break fi; od; if j<=n then a:=addcol(a,j,k); a:=addrow(a,j,k); fi; fi; if a[k,k]<>0 then for j from k+1 to n do x:=-a[k,j]/a[k,k]; a:=addcol(a,k,j,x);a:=addrow(a,k,j,x); od; fi; od; evalm(a); end;

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

princaxis(s);

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyIiITYkIiIjRiZGKjYkRidGLEYqNiRGLEYsISIiNiRGLEYnRio2JEYnRiZGKjYkRiZGJ0YqNiRGJkYmRiY2JEYmRixGKg==

<Text-field style="Heading 3" layout="Heading 3">1.2.35. Sylvester-f\303\251le tehetetlens\303\251gi t\303\251tel. </Text-field>

<Text-field style="Heading 3" layout="Heading 3">*1.2.36. Konjug\303\241lt biline\303\241ris lek\303\251pez\303\251sek.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">*1.2.37. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">*1.2.38. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">*1.2.39. Hermite-form\303\241k.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">*1.2.40. Multiline\303\241ris lek\303\251pez\303\251sek.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">*1.2.41. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">*1.2.42. P\303\251lda.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">*1.2.43. Tenzorok, tenzorszorzat.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">*1.2.44. Seg\303\251dt\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">*1.2.45. Tenzorok koordin\303\241t\303\241inak transzform\303\241ci\303\263ja.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">*1.2.46. Einstein-konvenci\303\263.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.47. Permut\303\241ci\303\263k.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.48. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.49. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.50. Ter\303\274let, t\303\251rfogat \303\251s determin\303\241ns.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.51. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.52. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">*1.2.53. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.54. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.55. M\303\241trix determin\303\241nsa.</Text-field>

a:=matrix(4,4); det(a);

PTYiNiQ7IiIiIiIlRiVFXFtsIQ==

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

<Text-field style="Heading 3" layout="Heading 3">1.2.56. T\303\251tel.</Text-field>

a:=matrix(1,1); det(a);

PTYiNiQ7IiIiRiZGJUVcW2wh

JkkiYUc2IjYkIiIiRiY=

a:=matrix(2,2); det(a);

PTYiNiQ7IiIiIiIjRiVFXFtsIQ==

LCYqJiZJImFHNiI2JCIiIkYoRigmRiU2JCIiI0YrRihGKComJkYlNiRGKEYrRigmRiU2JEYrRihGKCEiIg==

a:=matrix(3,3); det(a);

PTYiNiQ7IiIiIiIkRiVFXFtsIQ==

LC4qKCZJImFHNiI2JCIiIkYoRigmRiU2JCIiI0YrRigmRiU2JCIiJEYuRihGKCooRiRGKCZGJTYkRitGLkYoJkYlNiRGLkYrRighIiIqKCZGJTYkRitGKEYoJkYlNiRGKEYrRihGLEYoRjQqKEY2RigmRiU2JEYoRi5GKEYyRihGKCooJkYlNiRGLkYoRihGOEYoRjBGKEYoKihGPkYoRjtGKEYpRihGNA==

<Text-field style="Heading 3" layout="Heading 3">1.2.57. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.58. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.59. R\303\251szm\303\241trix, aldetermin\303\241ns.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.60. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.61. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.62. T\303\251tel.</Text-field>

a:=hilbert(3); det(a); gausselim(a,'ra','da'); da;

PUkqc3ltbWV0cmljRzYiNiQ7IiIiIiIkRiZFXFtsJzYkRihGKCNGJyIiJjYkIiIjRi4jRidGKDYkRi5GKCNGJyIiJTYkRidGKEYvNiRGJ0YnRic2JEYnRi4jRidGLg==

IyIiIiIlZ0A=

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyNGJiIkIT02JCIiI0YmIiIhNiRGJ0YtRi42JEYtRi0jRiYiIzc2JEYtRidGMTYkRidGJkYuNiRGJkYnI0YmRic2JEYmRiZGJjYkRiZGLSNGJkYt

IyIiIiIlZ0A=

<Text-field style="Heading 3" layout="Heading 3">1.2.63. Kifejt\303\251si t\303\251tel.</Text-field>

delcols(a,2..3);delrows(a,1..1);

PTYiNiQ7IiIiIiIkO0YmRiZFXFtsJDYkIiIjRiYjRiZGKzYkRidGJiNGJkYnNiRGJkYmRiY=

PTYiNiQ7IiIiIiIjO0YmIiIkRVxbbCc2JEYnRiYjRiZGKTYkRidGJyNGJiIiJTYkRidGKSNGJiIiJjYkRiZGKUYuNiRGJkYmI0YmRic2JEYmRidGLA==

delcols(delrows(a,1..1),1..1);A11:=minor(a,1,1);A12:=minor(a,1,2);A13:=minor(a,1,3);

PTYiNiQ7IiIiIiIjRiVFXFtsJTYkRidGJiNGJiIiJTYkRidGJyNGJiIiJjYkRiZGJiNGJiIiJDYkRiZGJ0Yq

PTYiNiQ7IiIiIiIjRiVFXFtsJTYkRidGJiNGJiIiJDYkRidGJyNGJiIiJjYkRiZGJiNGJkYnNiRGJkYnI0YmIiIl

PTYiNiQ7IiIiIiIjRiVFXFtsJTYkRidGJiNGJiIiJDYkRidGJyNGJiIiJTYkRiZGJiNGJkYnNiRGJkYnRio=

a[1,1]*det(A11)-a[1,2]*det(A12)+a[1,3]*det(A13);

IyIiIiIlZ0A=

<Text-field style="Heading 3" layout="Heading 3">*1.2.64. Line\303\241ris transzform\303\241ci\303\263 determin\303\241nsa.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">*1.2.65. Determin\303\241nsok szorz\303\241st\303\251tele.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.66. Determin\303\241nsok szorz\303\241st\303\251tele.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.67. Megjegyz\303\251s: line\303\241ris transzform\303\241ci\303\263 determin\303\241nsa.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.68. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.69. T\303\251tel.</Text-field>

b:=adjoint(a); evalm(a&*b);

PUkqc3ltbWV0cmljRzYiNiQ7IiIiIiIkRiZFXFtsJzYkRihGKCNGJyIjNzYkIiIjRi4jIiIlIiNYNiRGLkYoIyEiIkYsNiRGJ0YoI0YnIiNzNiRGJ0YnI0YnIiRTIzYkRidGLiNGNCIjZw==

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyNGJiIlZ0A2JCIiI0YmIiIhNiRGJ0YtRi42JEYtRi1GKjYkRi1GJ0YuNiRGJ0YmRi42JEYmRidGLjYkRiZGJkYqNiRGJkYtRi4=

<Text-field style="Heading 3" layout="Heading 3">1.2.70. Line\303\241ris egyenletek.</Text-field>

a:=matrix([[1,1,2,5,0],[0,1,1,3,-1],[1,0,1,2,1]]);

PTYiNiQ7IiIiIiIkO0YmIiImRVxbbDA2JEYnRidGJjYkIiIjRiYiIiE2JEYnRi1GLjYkRi1GLUYmNiRGLUYnRiY2JEYnRiZGJjYkRi0iIiVGJzYkRi1GKSEiIjYkRiZGJ0YtNiRGJkYmRiY2JEYmRi1GJjYkRiZGKUYuNiRGJ0Y0Ri02JEYmRjRGKTYkRidGKUYm

colspace(a); rank(a); kernel(a); coldim(a);

PCQ9NiI2IzsiIiIiIiRFXFtsJEYnRiciIiMiIiFGKEYnPUYkRiVFXFtsJEYnRitGKkYnRighIiI=

IiIj

PCU9NiI2IzsiIiIiIiZFXFtsJkYnISIiIiIjRioiIiRGJ0YoIiIhIiIlRi09RiRGJUVcW2wmRichIiNGKyEiJEYsRi1GKEYtRi5GJz1GJEYlRVxbbCZGJ0YqRitGJ0YsRi1GKEYnRi5GLQ==

IiIm

b:=vector([0,0,0]); linsolve(a,b);

PTYiNiM7IiIiIiIkRVxbbCRGJiIiISIiI0YpRidGKQ==

PTYiNiM7IiIiIiImRVxbbCZGJiwoJkkjX3RHRiM2I0YmISIiKiYiIiNGJiZGKzYjRi9GJkYtJkYrNiMiIiRGLUYvLChGKkYtKiZGNEYmRjBGJkYtRjJGJkY0RipGJ0YyIiIlRjA=

b:=vector([1,1,1]); linsolve(a,b);

PTYiNiM7IiIiIiIkRVxbbCRGJkYmIiIjRiZGJ0Ym

<Text-field style="Heading 3" layout="Heading 3">1.2.71. \303\201ll\303\255t\303\241s.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.72. A szuperpoz\303\255ci\303\263 elve.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.73. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.74. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.75. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.76. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.77. K\303\266vetkezm\303\251ny.</Text-field>

b:=vector([0,0,0]); linsolve(a,b);

PTYiNiM7IiIiIiIkRVxbbCRGJiIiISIiI0YpRidGKQ==

PTYiNiM7IiIiIiImRVxbbCZGJiwoJkkjX3RHRiM2I0YmISIiKiYiIiNGJiZGKzYjRi9GJkYtJkYrNiMiIiRGLUYvLChGKkYtKiZGNEYmRjBGJkYtRjJGJkY0RipGJ0YyIiIlRjA=

b:=vector([1,1,0]); linsolve(a,b);

PTYiNiM7IiIiIiIkRVxbbCRGJkYmIiIjRiZGJyIiIQ==

PTYiNiM7IiIiIiImRVxbbCZGJiwoJkkjX3RHRiM2IyIiIyEiIiomRi1GJiZGKzYjRiZGJkYuJkYrNiMiIiRGLkYtLCpGJkYmRipGLiomRjRGJkYwRiZGLkYyRiZGNEYqRidGMiIiJUYw

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

<Text-field style="Heading 3" layout="Heading 3">1.2.78. Invari\303\241ns alterek.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.79. Saj\303\241t\303\251rt\303\251k, saj\303\241tvektor, saj\303\241talt\303\251r.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.80. Karakterisztikus polinom.</Text-field>

a:=matrix([[1,2,I],[2,-I,3],[-1,2*I,4]]); evalm(-charmat(a,lambda)); det(%); (-1)^3*charpoly(a,lambda);

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyIiJTYkIiIjRiZGLDYkRidGLComRixGJl4jRiZGJjYkRixGLCwkRi8hIiI2JEYsRidGJzYkRidGJkYyNiRGJkYnRi82JEYmRiZGJjYkRiZGLEYs

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJywmSSdsYW1iZGFHRiMhIiIiIiVGJjYkIiIjRiZGLzYkRidGLyomRi9GJl4jRiZGJjYkRi9GLywmRitGLEYyRiw2JEYvRidGJzYkRidGJkYsNiRGJkYnRjI2JEYmRiYsJkYrRixGJkYmNiRGJkYvRi8=

LCwqJClJJ2xhbWJkYUc2IiIiJCIiIiEiIiomIiImRigpRiUiIiNGKEYoKiYsJF4jRihGKEYoRixGKEYpKiYqJiIjNUYoRjBGKEYoRiVGKEYoLCYiI0RGKUYyRilGKA==

<Text-field style="Heading 3" layout="Heading 3">1.2.81. T\303\251tel.</Text-field>

evalf(solve(%,lambda)); %[1]+%[2]+%[3]; trace(a);

NiUsJiQiK3EuXCZSJSEiKiIiIiomJCIrZSZ5Ok4iRiZGJ14jRidGJ0YnLCYkIitiQm9NQ0YmRicqJiQiKzxmdEg3RiZGJ0YrRichIiIsJiQiK0JGPEk9RiZGMiomJCIrVkUlPTciRiZGJ0YrRidGMg==

LCYkIistKysrXSEiKiIiIiomJCIrLSsrKzVGJUYmXiNGJkYmISIi

LCYiIiYiIiJeI0YkISIi

evalf(eigenvals(a));

NiUsJiQiK3EuXCZSJSEiKiIiIiomJCIrZSZ5Ok4iRiZGJ14jRidGJ0YnLCYkIitiQm9NQ0YmRicqJiQiKzxmdEg3RiZGJ0YrRichIiIsJiQiK0JGPEk9RiZGMiomJCIrVkUlPTciRiZGJ0YrRidGMg==

evalf(eigenvects(a));

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

<Text-field style="Heading 3" layout="Heading 3">1.2.82. Algebrai multiplicit\303\241s.</Text-field>

matrix([[1,1,0],[0,1,0],[0,0,5]]); eigenvects(%);

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyIiJjYkIiIjRiYiIiE2JEYnRixGLTYkRixGLEYmNiRGLEYnRi02JEYnRiZGLTYkRiZGJ0YtNiRGJkYmRiY2JEYmRixGJg==

NiQ3JSIiJiIiIjwjPTYiNiM7RiUiIiRFXFtsJEYlIiIhIiIjRi1GK0YlNyVGJUYuPCM9RihGKUVcW2wkRiVGJUYuRi1GK0Yt

a:=matrix([[1,1,0],[0,1,0],[0,0,1]]); eigenvects(%);

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJ0YmNiQiIiNGJiIiITYkRidGK0YsNiRGK0YrRiY2JEYrRidGLDYkRidGJkYsNiRGJkYnRiw2JEYmRiZGJjYkRiZGK0Ym

NyUiIiIiIiQ8JD02IjYjO0YjRiRFXFtsJEYjRiMiIiMiIiFGJEYsPUYnRihFXFtsJEYjRixGK0YsRiRGIw==

matrix([[1,1,0],[0,1,1],[0,0,1]]); eigenvects(%);

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJ0YmNiQiIiNGJiIiITYkRidGK0YsNiRGK0YrRiY2JEYrRidGJjYkRidGJkYsNiRGJkYnRiw2JEYmRiZGJjYkRiZGK0Ym

NyUiIiIiIiQ8Iz02IjYjO0YjRiRFXFtsJEYjRiMiIiMiIiFGJEYs

<Text-field style="Heading 3" layout="Heading 3">*1.2.83. Cayley-Hamilton-t\303\251tel.</Text-field>

a:=matrix([[1,0,0],[1,1,0],[0,0,2]]); p:=charpoly(a,lambda); expand(p); L:=PolynomialTools[CoefficientList](p,lambda); L:=zip((x,y)->x*y,L,[a&^i$i=0..nops(L)-1]); p:=convert(L,`+`); evalm(p);

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyIiIzYkRipGJkYmNiRGJ0YqIiIhNiRGKkYqRiY2JEYqRidGLTYkRidGJkYtNiRGJkYnRi02JEYmRiZGJjYkRiZGKkYt

KiYpLCZJJ2xhbWJkYUc2IiIiIkYnISIiIiIjRicsJkYlRidGKUYoRic=

LCoqJClJJ2xhbWJkYUc2IiIiJCIiIkYoKiYiIiVGKClGJSIiI0YoISIiKiYiIiZGKEYlRihGKEYsRi0=

NyYhIiMiIiYhIiUiIiI=

NyYsJComIiIjIiIiLUkjJl5HNiI2JEkiYUdGKSIiIUYmISIiLCQqJiIiJkYmLUYoNiRGK0YmRiZGJiwkKiYiIiVGJi1GKDYkRitGJUYmRi0tRig2JEYrIiIk

LCoqJiIiIyIiIi1JIyZeRzYiNiRJImFHRigiIiFGJSEiIiomIiImRiUtRic2JEYqRiVGJUYlKiYiIiVGJS1GJzYkRipGJEYlRiwtRic2JEYqIiIkRiU=

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyIiITYkIiIjRiZGKjYkRidGLEYqNiRGLEYsRio2JEYsRidGKjYkRidGJkYqNiRGJkYnRio2JEYmRiZGKjYkRiZGLEYq

<Text-field style="Heading 3" layout="Heading 3">1.2.84. Fels\305\221 h\303\241romsz\303\266g alak.</Text-field>

t:=matrix([[1,0,0],[0,1,2],[0,1,1]]); tm:=inverse(t); b:=evalm(tm&*a&*t);

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJ0YmNiQiIiNGJiIiITYkRidGK0YmNiRGK0YrRiY2JEYrRidGKzYkRidGJkYsNiRGJkYnRiw2JEYmRiZGJjYkRiZGK0Ys

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyEiIjYkIiIjRiYiIiE2JEYnRixGJjYkRixGLEYqNiRGLEYnRiw2JEYnRiZGLTYkRiZGJ0YtNiRGJkYmRiY2JEYmRixGLQ==

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyIiITYkIiIjRiYhIiI2JEYnRixGLTYkRixGLEYnNiRGLEYnRiw2JEYnRiZGJjYkRiZGJ0YqNiRGJkYmRiY2JEYmRixGKg==

eigenvects(b);

NiQ3JSIiIiIiIzwjPTYiNiM7RiQiIiRFXFtsJEYkIiIhRiUhIiJGK0YkNyVGJUYkPCM9RihGKUVcW2wkRiRGLUYlISIjRitGJA==

f11:=vector([0,-2,1]); e11:=vector([1,0,0]); e12:=vector([0,1,0]); e13:=vector([0,0,1]); basis([f11,e11,e12,e13]);

PTYiNiM7IiIiIiIkRVxbbCRGJiIiISIiIyEiI0YnRiY=

PTYiNiM7IiIiIiIkRVxbbCRGJkYmIiIjIiIhRidGKg==

PTYiNiM7IiIiIiIkRVxbbCRGJiIiISIiI0YmRidGKQ==

PTYiNiM7IiIiIiIkRVxbbCRGJiIiISIiI0YpRidGJg==

NyVJJGYxMUc2IkkkZTExR0YkSSRlMTJHRiQ=

t1:=matrix([[0,1,0],[-2,0,1],[1,0,0]]); t1m:=inverse(t1); bb:=evalm(t1m&*b&*t1);

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyIiITYkIiIjRiYhIiM2JEYnRixGKjYkRixGLEYqNiRGLEYnRiY2JEYnRiZGJjYkRiZGJ0YqNiRGJkYmRio2JEYmRixGJg==

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyIiIzYkRipGJkYmNiRGJ0YqRiY2JEYqRioiIiE2JEYqRidGLjYkRidGJkYuNiRGJkYnRiY2JEYmRiZGLjYkRiZGKkYu

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJ0YmNiQiIiNGJiIiITYkRidGK0YmNiRGK0YrRiY2JEYrRidGLDYkRidGJkYsNiRGJkYnISIiNiRGJkYmRis2JEYmRitGJg==

b1:=matrix([[1,0],[1,1]]); eigenvects(b1);

PTYiNiQ7IiIiIiIjRiVFXFtsJTYkRidGJkYmNiRGJ0YnRiY2JEYmRiZGJjYkRiZGJyIiIQ==

NyUiIiIiIiM8Iz02IjYjO0YjRiRFXFtsI0YjIiIhRiRGIw==

f22:=vector([0,1]); e22:=vector([1,0]); e23:=vector([0,1]); basis([f22,e22,e23]);

PTYiNiM7IiIiIiIjRVxbbCNGJiIiIUYnRiY=

PTYiNiM7IiIiIiIjRVxbbCNGJkYmRiciIiE=

PTYiNiM7IiIiIiIjRVxbbCNGJiIiIUYnRiY=

NyRJJGYyMkc2IkkkZTIyR0Yk

t2:=matrix([[0,1],[1,0]]); t2m:=inverse(t2); bb1:=evalm(t2m&*b1&*t2);

PTYiNiQ7IiIiIiIjRiVFXFtsJTYkRidGJkYmNiRGJ0YnIiIhNiRGJkYmRis2JEYmRidGJg==

PTYiNiQ7IiIiIiIjRiVFXFtsJTYkRidGJiIiITYkRidGJ0YmNiRGJkYmRiY2JEYmRidGJg==

b2:=matrix([[1]]); eigenvects(b2);

PTYiNiQ7IiIiRiZGJUVcW2wiNiRGJkYmRiY=

NyUiIiJGIzwjPTYiNiM7RiNGI0VcW2wiRiNGIw==

f23:=1*e22; print(f23);

SSRlMjJHNiI=

print(f11); f12:=0*e11+1*e12; print(f12); f13:=1*e11+0*e12; print(f13);

SSRmMTFHNiI=

SSRlMTJHNiI=

SSRlMTFHNiI=

t:=matrix([[0,0,1],[-2,1,0],[1,0,0]]); tm:=inverse(t); print(evalm(tm&*b&*t));

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyIiITYkIiIjRiYhIiM2JEYnRixGKjYkRixGLEYmNiRGLEYnRio2JEYnRiZGJjYkRiZGJ0YmNiRGJkYmRio2JEYmRixGKg==

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyIiITYkIiIjRiZGKjYkRidGLEYqNiRGLEYsRiY2JEYsRidGLDYkRidGJkYmNiRGJkYnRiY2JEYmRiZGKjYkRiZGLEYq

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJ0YmNiQiIiNGJiIiITYkRidGK0YsNiRGK0YrRiY2JEYrRidGJjYkRidGJkYsNiRGJkYnRiY2JEYmRiZGKzYkRiZGKyEiIg==

<Text-field style="Heading 3" layout="Heading 3">1.2.85. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.86. Seg\303\251dt\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.2.87. \303\201tl\303\263s alak.</Text-field>

a:=matrix([[2,0,0],[0,1,0],[0,0,3]]); t:=matrix([[1,-4,3],[1,-2,2],[3,-3,-2]]); tm:=inverse(t); b:=evalm(tm&*a&*t);

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJ0YnNiQiIiNGJiIiITYkRidGK0YsNiRGK0YrRiY2JEYrRidGLDYkRidGJkYsNiRGJkYnRiw2JEYmRiZGKzYkRiZGK0Ys

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyEiIzYkIiIjRiZGJjYkRidGLCEiJDYkRixGLEYqNiRGLEYnRiw2JEYnRiZGJzYkRiZGJ0YnNiRGJkYmRiY2JEYmRiwhIiU=

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyMhIiMiIzg2JCIiI0YmIyEiKUYsNiRGJ0YuIyIiKkYsNiRGLkYuIyIjNkYsNiRGLkYnIyEiIkYsNiRGJ0YmIyEiJEYsNiRGJkYnI0YuRiw2JEYmRiYjISM1Riw2JEYmRi4jIiM8Riw=

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJyMiIzciIzg2JCIiI0YmIyEjOUYsNiRGJ0YuIyIjQ0YsNiRGLkYuIyIjXkYsNiRGLkYnIyEjP0YsNiRGJ0YmIyEjOkYsNiRGJkYnIyEjUUYsNiRGJkYmIyIjOkYsNiRGJkYuIyIjR0Ys

L:=eigenvects(b); b1:=op(1,L[1][3]); b2:=op(1,L[2][3]); b3:=op(1,L[3][3]); tb:=augment(b1,b2,b3); evalm(inverse(tb)&*b&*tb);

NiU3JSIiJCIiIjwjPTYiNiM7RiVGJEVcW2wkRiUhIiMiIiNGJUYkRi03JUYtRiU8Iz1GKEYpRVxbbCRGJSMiIzVGJEYtIyIiKUYkRiRGJTclRiVGJTwjPUYoRilFXFtsJEYlIyIjPCIiKkYtIyIjNkY8RiRGJQ==

PTYiNiM7IiIiIiIkRVxbbCRGJiEiIyIiI0YmRidGKg==

PTYiNiM7IiIiIiIkRVxbbCRGJiMiIzVGJyIiIyMiIilGJ0YnRiY=

PTYiNiM7IiIiIiIkRVxbbCRGJiMiIzwiIioiIiMjIiM2RitGJ0Ym

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJ0YmNiQiIiNGJkYmNiRGJ0YrRiY2JEYrRisjIiIpRic2JEYrRicjIiM2IiIqNiRGJ0YmRis2JEYmRicjIiM8RjM2JEYmRiYhIiM2JEYmRisjIiM1Ric=

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJ0YmNiQiIiNGJiIiITYkRidGK0YsNiRGK0YrRis2JEYrRidGLDYkRidGJkYsNiRGJkYnRiw2JEYmRiZGJzYkRiZGK0Ys

<Text-field style="Heading 2" layout="Heading 2">1.3. Bels\305\221 szorzat</Text-field>

restart;with(linalg);

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

<Text-field style="Heading 3" layout="Heading 3">1.3.1. Norma.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.3.2. P\303\251ld\303\241k.</Text-field>

x:=vector([1,1,1]); norm(x,1), norm(x,1.5), norm(x,2), norm(x,3), norm(x,infinity), norm(x); evalf(%);

PTYiNiM7IiIiIiIkRVxbbCRGJkYmIiIjRiZGJ0Ym

NigiIiQkIitCUTMhMyMhIioqJClGIyMiIiIiIiNGKiokKUYjI0YqRiNGKkYqRio=

NigkIiIkIiIhJCIrQlEzITMjISIqJCIrMzMwSzxGKCQiK3EmXEFXIkYoJCIiIkYlRi0=

y:=vector([1,2,3+4*I]); norm(y,1), norm(y,1.5), norm(y,2), norm(y,3), norm(y,infinity), norm(y);evalf(%);

PTYiNiM7IiIiIiIkRVxbbCRGJkYmIiIjRilGJywmRidGJiomIiIlRiZeI0YmRiZGJg==

NigiIikkIituO2QlMychIioqJCkiI0kjIiIiIiIjRisqJCkiJE0iI0YrIiIkRisiIiZGMg==

NigkIiIpIiIhJCIrbjtkJTMnISIqJCIrdmJBeGFGKCQiK1oqSHM2JkYoJCIiJkYlRi0=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

<Text-field style="Heading 3" layout="Heading 3">1.3.3. Bels\305\221 szorzat.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.3.4. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.3.5. P\303\251lda.</Text-field>

dotprod(x,y); dotprod(y,x);

LCYiIiciIiIqJiIiJUYkXiNGJEYkISIi

LCYiIiciIiIqJiIiJUYkXiNGJEYkRiQ=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

<Text-field style="Heading 3" layout="Heading 3">1.3.6. Megjegyz\303\251s.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.3.7. Sz\303\266gek, euklid\303\251szi t\303\251r, unit\303\251r t\303\251r.</Text-field>

y:=vector([1,-1,0]); angle(x,y); angle(y,x);

PTYiNiM7IiIiIiIkRVxbbCRGJkYmIiIjISIiRiciIiE=

LCQqJiMiIiIiIiNGJUkjUGlHJSpwcm90ZWN0ZWRHRiVGJQ==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

<Text-field style="Heading 3" layout="Heading 3">1.3.8. Defin\303\255ci\303\263.</Text-field>

z:=vector([2,3,4]); dotprod(x,y); dotprod(y,z);

PTYiNiM7IiIiIiIkRVxbbCRGJiIiI0YpRidGJyIiJQ==

IiIh

ISIi

<Text-field style="Heading 3" layout="Heading 3">1.3.9. Vegyes szorzat.</Text-field>

dotprod(x,crossprod(y,z)); det(augment(x,y,z));

ISIk

<Text-field style="Heading 3" layout="Heading 3">1.3.10. \303\201ltal\303\241nos\303\255tott Pythagorasz-t\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.3.11. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.3.12. Gram-Schmidt-ortogonaliz\303\241l\303\241s.</Text-field>

basis([z,y,x]);

NyVJInpHNiJJInlHRiRJInhHRiQ=

GramSchmidt([z,y,x]);

NyU3JSIiIyIiJCIiJTclIyIjSiIjSCMhI0VGKiNGJkYqNyUjRiYiIz5GLyMhIiZGMA==

L:=map(normalize,%);

NyU9NiI2IzsiIiIiIiRFXFtsJEYnLCQqJiMiIiMiI0hGJylGLiNGJ0YtRidGJ0YtLCQqJiNGKEYuRidGL0YnRidGKCwkKiYjIiIlRi5GJ0YvRidGJz1GJEYlRVxbbCRGJywkKigjIiNKIiVgO0YnKSIjZEYwRidGL0YnRidGLSwkKigjIiNFRj5GJ0Y/RidGL0YnISIiRigsJCooI0Y3Rj5GJ0Y/RidGL0YnRic9RiRGJUVcW2wkRicsJCooI0Y3RkBGJylGKEYwRicpIiM+RjBGJ0YnRi1GS0YoLCQqKCMiIiZGQEYnRk5GJ0ZPRidGRQ==

map(norm,L,2);

NyUiIiJGI0Yj

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

<Text-field style="Heading 3" layout="Heading 3">1.3.13. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.3.14. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.3.15. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.3.16. Az approxim\303\241ci\303\263 alapfeladata norm\303\241lt t\303\251rben.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.3.17. Legjobb line\303\241ris approxim\303\241ci\303\263 bels\305\221 szorzat t\303\251rben.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.3.18. K\303\266vetkezm\303\251ny: Bessel-egyenl\305\221tlens\303\251g.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.3.19. Ortogon\303\241lis felbont\303\241si t\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.3.20. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.3.21. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.3.22. El\305\221\303\241ll\303\255t\303\241si t\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.3.23. Adjung\303\241lt lek\303\251pez\303\251s.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.3.24. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.3.25. Adjung\303\241lt oper\303\241tor m\303\241trixa.</Text-field>

a:=matrix([[1,2,I],[2,-I,3]]); htranspose(a);

PTYiNiQ7IiIiIiIjO0YmIiIkRVxbbCc2JEYmRiZGJjYkRiZGJ0YnNiRGJ0YpRik2JEYmRileI0YmNiRGJ0YnLCRGLyEiIjYkRidGJkYn

PTYiNiQ7IiIiIiIkO0YmIiIjRVxbbCc2JEYnRiYsJF4jRiYhIiI2JEYmRiZGJjYkRiZGKUYpNiRGJ0YpRic2JEYpRilGLTYkRilGJkYp

d:=matrix(L); ds:=htranspose(d);

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJiwkKigjIiIlIiNkRiYpRicjRiYiIiNGJikiIz5GMEYmRiY2JEYmRiYsJComI0YxIiNIRiYpRjhGMEYmRiY2JEYmRjEsJComI0YnRjhGJkY5RiZGJjYkRjFGJywkKigjRi0iJWA7RiYpRi5GMEYmRjlGJkYmNiRGJ0YxRio2JEYmRicsJComI0YtRjhGJkY5RiZGJjYkRidGJywkKigjIiImRi5GJkYvRiZGMkYmISIiNiRGMUYxLCQqKCMiI0VGQkYmRkNGJkY5RiZGTjYkRjFGJiwkKigjIiNKRkJGJkZDRiZGOUYmRiY=

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJiwkKiYjIiIlIiNIRiYpRi4jRiYiIiNGJkYmNiRGJkYmLCQqJiNGMUYuRiZGL0YmRiY2JEYmRjEsJCooIyIjSiIlYDtGJikiI2RGMEYmRi9GJkYmNiRGMUYnLCQqKCNGLUY9RiYpRidGMEYmKSIjPkYwRiZGJjYkRidGMSwkKigjRi1GO0YmRjxGJkYvRiZGJjYkRiZGJ0Y/NiRGJ0YnLCQqKCMiIiZGPUYmRkJGJkZDRiYhIiI2JEYxRjEsJCooIyIjRUY7RiZGPEYmRi9GJkZPNiRGMUYmLCQqJiNGJ0YuRiZGL0YmRiY=

evalm(d&*ds); evalm(ds&*d);

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJiIiITYkRiZGJkYmNiRGJiIiI0YqNiRGLUYnRio2JEYnRi1GKjYkRiZGJ0YqNiRGJ0YnRiY2JEYtRi1GJjYkRi1GJkYq

<Text-field style="Heading 3" layout="Heading 3">1.3.26. \303\226nadjung\303\241lt \303\251s norm\303\241lis transzform\303\241ci\303\263k.</Text-field>

b:=matrix([[1,2,I],[2,3,-3*I],[-I,3*I,-1]]); bs:=htranspose(b);

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJiwkXiNGJiEiIjYkRiZGJkYmNiRGJiIiI0YvNiRGL0YnLCQqJkYnRiZGK0YmRiw2JEYnRi9GMjYkRiZGJ0YrNiRGJ0YnRiw2JEYvRi9GJzYkRi9GJkYv

evalm(b&*bs); evalm(bs&*b);

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJiomIiInRiZeI0YmRiY2JEYmRiZGKzYkRiYiIiMiIiY2JEYvRicsJComIiIlRiZGLEYmISIiNiRGJ0YvRjM2JEYmRicsJEYqRjU2JEYnRiciIzY2JEYvRi8iI0E2JEYvRiZGMA==

c:=matrix([[I,2,1],[-2,3*I,4],[-1,-4,0]]); cs:=htranspose(c);

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJiEiIjYkRiZGJl4jRiY2JEYmIiIjRi42JEYuRiciIiU2JEYnRi4hIiU2JEYmRidGJjYkRidGJyIiITYkRi5GLiomRidGJkYsRiY2JEYuRiYhIiM=

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJkYmNiRGJkYmLCReI0YmISIiNiRGJiIiIyEiIzYkRi9GJyEiJTYkRidGLyIiJTYkRiZGJ0YtNiRGJ0YnIiIhNiRGL0YvLCQqJkYnRiZGLEYmRi02JEYvRiZGLw==

evalm(c&*cs); evalm(cs&*c);

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJiwmIiIpISIiXiNGJkYmNiRGJkYmIiInNiRGJiIiIywmIiIlRiYqJkYrRiZGLUYmRiw2JEYxRicsJkYxRiYqJiIjN0YmRi1GJkYsNiRGJ0YxLCZGMUYmRjdGJjYkRiZGJywmRitGLEYtRiw2JEYnRiciIzw2JEYxRjEiI0g2JEYxRiYsJkYzRiZGNEYm

<Text-field style="Heading 3" layout="Heading 3">1.3.27. P\303\251lda.</Text-field>

a:=matrix([[1,2,I],[2,-I,3],[-1,2*I,4]]); as:=htranspose(a);

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJiEiIjYkRiZGJkYmNiRGJiIiI0YtNiRGLUYnRic2JEYnRi0qJkYtRiZeI0YmRiY2JEYmRidGMTYkRidGJyIiJTYkRi1GLSwkRjFGKjYkRi1GJkYt

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJiwkXiNGJiEiIjYkRiZGJkYmNiRGJiIiI0YvNiRGL0YnLCQqJkYvRiZGK0YmRiw2JEYnRi9GJzYkRiZGJ0YsNiRGJ0YnIiIlNiRGL0YvRis2JEYvRiZGLw==

evalm(a&*as); evalm(as&*a);

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJiEiIjYkRiZGJiIiJzYkRiYiIiMsJkYuRiYqJiIiJkYmXiNGJkYmRiY2JEYuRiciIik2JEYnRi5GNDYkRiZGJ0YqNiRGJ0YnIiNANiRGLkYuIiM5NiRGLkYmLCZGLkYmRjBGKg==

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJiwmIiIjRiZeI0YmISIiNiRGJkYmIiInNiRGJkYrLCZGK0YmKiYiIiVGJkYsRiZGLTYkRitGJywkKiZGJ0YmRixGJkYtNiRGJ0YrRjY2JEYmRicsJkYrRiZGLEYmNiRGJ0YnIiNFNiRGK0YrIiIqNiRGK0YmLCZGK0YmRjJGJg==

<Text-field style="Heading 3" layout="Heading 3">1.3.28.Polariz\303\241ci\303\263s formula.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.3.29. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.3.30. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.3.31. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.3.32. Megjegyz\303\251s.</Text-field>

orthog(d); orthog(ds);

SSV0cnVlRyUqcHJvdGVjdGVkRw==

<Text-field style="Heading 3" layout="Heading 3">1.3.33. T\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.3.34. Fels\305\221 h\303\241romsz\303\266g alak.</Text-field>

a:=map(evalf,a); as:=map(evalf,as); eigenvects(as); e3:=normalize(op(1,%[1][3]));

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJiQhIiIiIiE2JEYmRiYkRiZGLDYkRiYiIiMkRjBGLDYkRjBGJyRGJ0YsNiRGJ0YwKiZGMUYmXiNGJkYmNiRGJkYnKiZGLkYmRjZGJjYkRidGJyQiIiVGLDYkRjBGMCwkRjhGKzYkRjBGJkYx

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJiwkKiYkRiYiIiFGJl4jRiZGJiEiIjYkRiZGJkYsNiRGJiIiIyRGMkYtNiRGMkYnLCQqJkYzRiZGLkYmRi82JEYnRjIkRidGLTYkRiZGJyRGL0YtNiRGJ0YnJCIiJUYtNiRGMkYyRis2JEYyRiZGMw==

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

PTYiNiM7IiIiIiIkRVxbbCRGJiwmJCIrNG48PT0hIzVGJiomJCIrUD91ZjxGLEYmXiNGJkYmISIiIiIjLCYkIittU2gkUiVGLEYmKiYkIitKO3Q6cyEjNkYmRjBGJkYxRicsJiQiKz5pMCMqXEYsRiYqJiQiK2olXCUqKXBGLEYmRjBGJkYm

f11:=vector([1,0,0]); c1:=dotprod(f11,e3); g11:=normalize(evalm(f11-c1*e3));

PTYiNiM7IiIiIiIkRVxbbCRGJkYmIiIjIiIhRidGKg==

LCYkIis0bjw9PSEjNSIiIiomJCIrUD91ZjxGJUYmXiNGJkYmRiY=

PTYiNiM7IiIiIiIkRVxbbCRGJiwmJCIrUkFldScqISM1RiYqJiQiIiFGL0YmXiNGJkYmRiYiIiMsJiQiK3UpZiZwJiohIzYhIiIqJiQiK05YaE5tRjVGJkYwRiZGNkYnLCYkIistU2dKTEY1RiYqJiQiK2JDZEBBRixGJkYwRiZGNg==

f12:=vector([0,1,0]); c1:=dotprod(f12,e3); c2:=dotprod(f12,g11); g12:=normalize(evalm(f12-c1*e3-c2*g11));

PTYiNiM7IiIiIiIkRVxbbCRGJiIiISIiI0YmRidGKQ==

LCYkIittU2gkUiUhIzUiIiIqJiQiK0o7dDpzISM2RiZeI0YmRiZGJg==

LCYkIit1KWYmcCYqISM2ISIiKiYkIitOWGhObUYlIiIiXiNGKkYqRio=

PTYiNiM7IiIiIiIkRVxbbCRGJiwmJCIrNyYzNSwqISM/RiYqJiQiKyVRYyNlbkYsRiZeI0YmRiYhIiIiIiMsJiQiK3QmSCF5KSkhIzVGJiomJCIiIUY5RiZGMEYmRiZGJywmJCIrKnljRC4jRjZGMSomJCIrci0zSFRGNkYmRjBGJkYx

a1:=matrix(2,2):a1[1,1]:=dotprod(multiply(a,g11),g11): a1[2,1]:=dotprod(multiply(a,g11),g12): a1[1,2]:=dotprod(multiply(a,g12),g11): a1[2,2]:=dotprod(multiply(a,g12),g12): print(a1);a1s:=htranspose(a1);

SSNhMUc2Ig==

PTYiNiQ7IiIiIiIjRiVFXFtsJTYkRiZGJiwmJCIrMjQhPS4iISIqRiYqJiQiKyl5JlJGNSEjNUYmXiNGJkYmRiY2JEYmRicsJiQiK2JuPE9CRi1GJiomJCIrSidSJ29kRjFGJkYyRiZGJjYkRidGJywmJCIrVEYiSEYlRjEhIiIqJiQiK3oqUSlbQUYtRiZGMkYmRiY2JEYnRiYsJiQiKyRmRkBFI0YtRiYqJiQiKzRZIzQ1I0YxRiZGMkYmRiY=

eigenvects(a1s); f2:=op(1,%[1][3]); e2:=normalize(evalm(f2[1]*g11+f2[2]*g12));

NiQ3JSwmJCIrY0JvTUMhIioiIiIqJiQiKztmdEg3RidGKF4jRihGKEYoRig8Iz02IjYjO0YoIiIjRVxbbCNGKCwmJCIrdFEqKTR3ISM1RigqJiQiKz82eCVcI0Y3RihGLEYoISIiRjIsJiQiK3BqQFpmRjdGKComJCIraCUqXFdxISM2RihGLEYoRig3JSwmJCIrQUY8ST1GJ0Y7KiYkIitXRSU9NyJGJ0YoRixGKEYoRig8Iz1GL0YwRVxbbCNGKCwmJCIrbHBvSm9GN0Y7KiYkIitSbS84PEY3RihGLEYoRjtGMiwmJCIrclNZKFEpRjdGKComJCIrZF9sX0hGN0YoRixGKEY7

PTYiNiM7IiIiIiIjRVxbbCNGJiwmJCIrdFEqKTR3ISM1RiYqJiQiKz82eCVcI0YsRiZeI0YmRiYhIiJGJywmJCIrcGpAWmZGLEYmKiYkIitoJSpcV3EhIzZGJkYwRiZGJg==

PTYiNiM7IiIiIiIkRVxbbCRGJiwmJCIrNldEaXQhIzVGJiomJCIrUG9lOENGLEYmXiNGJkYmISIiIiIjLCYkIitNJnpoUSVGLEYmKiYkIit2OCk9ZiQhIzZGJkYwRiZGJkYnLCYkIis6Q2o9N0YsRjEqJiQiKyd5WERQJUYsRiZGMEYmRjE=

f21:=vector([1,0,0]); c1:=dotprod(f21,e2); c2:=dotprod(f21,e3); e1:=normalize(evalm(f21-c1*e2-c2*e3));

PTYiNiM7IiIiIiIkRVxbbCRGJkYmIiIjIiIhRidGKg==

LCYkIis2V0RpdCEjNSIiIiomJCIrUG9lOENGJUYmXiNGJkYmRiY=

LCYkIis0bjw9PSEjNSIiIiomJCIrUD91ZjxGJUYmXiNGJkYmRiY=

PTYiNiM7IiIiIiIkRVxbbCRGJiwmJCIremkhUnomISM1RiYqJiQiIiFGL0YmXiNGJkYmRiYiIiMsJiQiK2FXdkBxRiwhIiIqJiQiKyFSKGUiUiRGLEYmRjBGJkY1RicsJiQiKyJRT0skRyEjNkYmKiYkIis7bUNhQkYsRiZGMEYmRiY=

ta:=augment(e1,e2,e3); evalm(inverse(ta)&*a&*ta);

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

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJiwmJCIjOCEjNUYmKiYkIiIlRi1GJl4jRiZGJkYmNiRGJkYmLCYkIis/RjxJPSEiKiEiIiomJCIrV0UlPTciRjZGJkYxRiZGNzYkRiYiIiMsJiQiKy5IJyl6JipGLUYmKiYkIitPMyNSMiNGNkYmRjFGJkYmNiRGPEYnLCYkIitlJ0d2bilGLUY3KiYkIit2OyZbNiJGNkYmRjFGJkYmNiRGJ0Y8LCYkRiZGNkYmKiYkRjxGNkYmRjFGJkY3NiRGJkYnLCYkIisnNFZfRiZGLUY3KiYkIishW25WZSZGLUYmRjFGJkY3NiRGJ0YnLCYkIitvLlwmUiVGNkYmKiYkIitjJnk6TiJGNkYmRjFGJkYmNiRGPEY8LCYkIitfQm9NQ0Y2RiYqJiQiKzdmdEg3RjZGJkYxRiZGNzYkRjxGJiwmJCIjUUYtRjcqJiQiIzdGLUYmRjFGJkY3

<Text-field style="Heading 3" layout="Heading 3">1.3.35. Seg\303\251dt\303\251tel.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.3.36. Norm\303\241lis transzform\303\241ci\303\263 \303\241tl\303\263s alakja.</Text-field>

print(b); Lb:=evalf(eigenvects(b));

SSJiRzYi

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

b1:=op(1,Lb[1][3]); b2:=op(1,Lb[2][3]); b3:=op(1,Lb[3][3]); tb:=augment(normalize(b1),normalize(b2),normalize(b3)); evalm(inverse(tb)&*b&*tb);

PTYiNiM7IiIiIiIkRVxbbCRGJiRGJiIiISIiIywmJCIrd3UhM2YjISIqRiYqJiQiKzdzeWV6ISM+RiZeI0YmRiYhIiJGJywmJCIrXHpSdyopRjNGJiomJCIrP2VrOzZGL0YmRjRGJkYm

PTYiNiM7IiIiIiIkRVxbbCRGJiRGJiIiISIiIywmJCIrZ04nZUEiISIqISIiKiYkIipORz4jeiEjPkYmXiNGJkYmRjBGJywmJCIrRmFeJD4nRjRGMComJCIrRz9uWz5GL0YmRjVGJkYm

PTYiNiM7IiIiIiIkRVxbbCRGJiRGJiIiISIiIywmJCIrcXpcJ0giISM1ISIiKiYkIitHZlwpKVshIz5GJl4jRiZGJkYmRicsJiQiKnZbUU0jRjRGMComJCIrTGhIWmZGL0YmRjVGJkYw

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJiwmJCIrKzYlKikqSCEjPkYmKiYkIiszQmlJUCEjNUYmXiNGJkYmRiY2JEYmRiYkIitwIj00TSRGMTYkRiYiIiMkIiskM3ZTKVJGMTYkRjdGJywmJCIrIiplWTI2RjEhIiIqJiQiK01KdXZURi1GJkYyRiZGJjYkRidGNywmJCIrXElhbkNGLUY+KiYkIitzY2xqeEYxRiZGMkYmRiY2JEYmRickIitsJHo+YSlGMTYkRidGJywmJCIrbTI2LT8hIz9GPiomJCIrJjNvLDMmRjFGJkYyRiZGPjYkRjdGNywmJCIrbEMkUilbRjFGPiomJCIrTmQ6Y0pGUEYmRjJGJkY+NiRGN0YmLCYkIitwZG5iJylGMUYmKiYkIishb2wqZUVGLUYmRjJGJkY+

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJiwmJCIjOCEjNUYmKiYkIitXPkMheSchIz5GJl4jRiZGJiEiIjYkRiZGJiwmJCIrSyJwXDEmISIqRiYqJiQiIiFGO0YmRjJGJkYmNiRGJiIiIywmJEY9RjhGMyomJCIrKDNYLFsmRjFGJkYyRiZGJjYkRj1GJywmJEYmRjhGJiomJCIrcSVcQCMqKUYxRiZGMkYmRiY2JEYnRj0sJiQiIzZGLUYmKiYkIiswOTNyZEYxRiZGMkYmRjM2JEYmRicsJiRGJ0YtRjMqJiQiK2trJmVQIiEjPUYmRjJGJkYmNiRGJ0YnLCYkIis+K1ZOOEY4RiYqJiQiIiZGMUYmRjJGJkYmNiRGPUY9LCYkIitdIipSK01GOEYzKiYkIiInRjFGJkYyRiZGMzYkRj1GJiwmJEZnbkYtRiYqJiQiKzIhKVI7KClGMUYmRjJGJkYm

print(c); evalf(eigenvects(c));

SSJjRzYi

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

map(evalf,d); Ld:=eigenvects(%); abs(Ld[1][1]); abs(Ld[2][1]); abs(Ld[3][1]);

PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRidGJiQiK0klSCIpSCYhIzU2JEYmRiYkIitqbiFSciRGLDYkRiYiIiMkIitaLCczZCZGLDYkRjFGJyQiK2UkeiRRKSohIzY2JEYnRjFGKjYkRiZGJyQiK0dOInlVKEYsNiRGJ0YnJCErKXloRWknRiw2JEYxRjEkISsmZVlcUidGLDYkRjFGJiQiKyxTdUN3Riw=

NiU3JSwmJCIrRDMmPWwqISM1ISIiKiYkIishKil5Y2gjRiciIiJeI0YsRixGLEYsPCM9NiI2IztGLCIiJEVcW2wkRiwsJiQiKylRQDdsJUYnRiwqJiQiK1IlR3dTJUYnRixGLUYsRigiIiMsJiQiK3lmPEg1ISIqRigqJiQiK2JHcCMzIkYnRixGLUYsRihGMywmJCIrKEgkXDkhKiEjNkYsKiYkIit5MTZRNUY/RixGLUYsRiw3JSQiKikqKioqKioqKkY/Riw8Iz1GMEYxRVxbbCRGLCQhKlxNUSEqKUY/RjskISstPkMmUiVGJ0YzJCErc2AhKVFVRic3JSwmRiVGKEYpRihGLDwjPUYwRjFFXFtsJEYsLCZGNkYsRjhGLEY7LCZGPUYoRkBGLEYzLCZGREYsRkdGKA==

JCIrLSsrKzUhIio=

JCIqKSoqKioqKioqISIq

JCIrLSsrKzUhIio=

<Text-field style="Heading 3" layout="Heading 3">1.3.37. K\303\266vetkezm\303\251ny.</Text-field>

<Text-field style="Heading 3" layout="Heading 3">1.3.38. Szimmetrikus transzform\303\241ci\303\263 \303\241tl\303\263s alakja.</Text-field>