f(x,y):= for i from 1 thru 9 do(
if (i > 6) then return(i)
);

A: matrix(
[0,1,2],
[0,3,0],
[1,0,0]
);

for i from 1 thru 3 do(
A[2,i]: A[2,i]-3*A[1,i]
);

A;
A*A;
A.A;
A^2;
A^^2;


load(diag);
load(eigen);


A: matrix(
[0,1,2],
[0,3,0],
[0,4,2]
);

/*
A:genmatrix(lambda ([i, j], -9 + random(10)),3,4);
*/

echelon(A);
triangularize(A);

A.matrix([x],[y],[z]);
transpose(%);
args(%);
%[1];
solve(%,[x,y,z]);

lahendid: matrix(
[c,0,0]
);

A.transpose(lahendid);

A: matrix(
[1,-1,1],
[1,1,-1],
[0,-1,2]
);

A: matrix(
[3,12,-4],
[-1,-3,1],
[-1,-12,6]
);


p:factor(charpoly(A,x));
p:factor(determinant(A-x*ident(3)));
solve(p=0,x);

eivals(A);
eivects(A);

jordan(A);
dispJordan(%);
C:ModeMatrix(A);

invert(C).A.C;

nondiagonalizable;

sims: simtran(A);

rank(A-3*ident(3));
A-3*ident(3);
%.matrix([x],[y],[z]);
transpose(%);
args(%);
%[1];
solve(%,[x,y,z]);
sols:%[1];
lahA: matrix([ev(x,%)],[ev(y,%)],[ev(z,%)]);
(A-3*ident(3)).lahA;

A: matrix(
[1,-2,2,-3],
[2,-3,2,4],
[0,0,1,0],
[0,0,0,1]
);

rank(A);

F(x,y):= 1*x[1]*y[1] + 2*x[2]*y[2] + 3*x[3]*y[3] + 4*x[4]*y[4];

sols: gramschmidt(A);
gramschmidt(A,F);

inprod(A[1],A[2]);

inprod(sols[1],sols[1]);
inprod(sols[1],sols[2]);
inprod(sols[1],sols[3]);
inprod(sols[1],sols[4]);
inprod(sols[2],sols[2]);
inprod(sols[2],sols[3]);
inprod(sols[2],sols[4]);
inprod(sols[3],sols[3]);
inprod(sols[3],sols[4]);
inprod(sols[4],sols[4]);

A: matrix(
[0,1,2],
[0,3,0],
[1,0,0]
);

kill(p);
p = 7;
echelon(A);
triangularize(A);
modulus;
echelon(A), modulus = 3;
triangularize(A), modulus = 3;
modulus;