?RandomInteger

Djelovanje linearnog operatora na skup vektora

SeedRandom[3]
A={{1,0},{0,-1}};
m=10;L=-2;R=8; (* m tocaka u segmentu [L,R] *)
p=RandomInteger[{L,R},{m,2}];
Print["A= ",MatrixForm[A],",   P:",Transpose[p]//MatrixForm]
sl1=ListPlot[p,PlotStyle->{Hue[.1],AbsolutePointSize[5]}];
Ap=p.A; (* transformacija tocaka matricom A *)
Print["A(P):",Transpose[Ap]//MatrixForm]
sl2=ListPlot[Ap,PlotStyle->{Hue[.2],AbsolutePointSize[5]}];
Show[sl1,sl2,AspectRatio->1]

?Polygon

Djelovanje linearnog operatora na geometrijski lik

al=-1; be=-1;
A={{al,0},{0,be}};
p={{1,1},{3,1},{5,2},{2,3},{1,2},{1,1}};
Lik=Polygon[p]; (* zadavanje geometrijskog lika u ravnini *)
sl1=Show[Graphics[{Thick,Hue[.1],Lik}],Frame->False,Axes->True,Ticks->Automatic];
Ap=p.A; (* transformacija tocaka matricom A *)
ALik=Polygon[Ap];
sl2=Show[Graphics[{Thick,Hue[.2],ALik}],Frame->False,Axes->True,Ticks->Automatic];
Show[sl2,sl1,PlotRange->{{-5,5},{-5,5}}]

Djelovanje linearnog operatora na kruznicu x1^2 + x2^2 == 1

al=3;be=.5;
ContourPlot[{x1^2+x2^2==1,(x1/al)^2+(x2/be)^2==1},{x1,-3,3},{x2,-3,3}]

ContourPlot[{x1^2+x2^2==1,(2x1/3-x2/3)^2+(-x1/3+2x2/3)^2==1},{x1,-3,3},{x2,-3,3}]