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charpoly-expand-matrix

a: matrix ([0.75,0.05...

expand(charpoly(a,x));

Calculate

charpoly-eigenvectors-matrix-ratsimp-solve

A:matrix([1,1,1,1],[-...

B:A.A;

Pol:charpoly(B,t);

Calculate

charpoly-expand-matrix

A:matrix([2,1+t,1],[1...

charpoly(A,x);

expand(%o2);

Calculate

charpoly-matrix

a: matrix([1, -1],[2,...

charpoly(a,x);

Calculate

charpoly-invert-matrix

m: matrix([3,-2,0],[0...

charpoly(m,x);

invert(m);

Calculate

charpoly-eigenvalues-expand-invert-matrix

M: matrix([1/2, -1/4]...

I: matrix([1, 0],[0,1]);

eigenvalues(M);

Calculate

charpoly-coeff-matrix-ratexpand-solve

A:matrix([2,1+t,0],[1...

expr:charpoly(A,x);

expr2:ratexpand(expr);

Calculate

charpoly-expand-matrix

A:matrix([2,1+t,1],[1...

charpoly(A,x);

expand(%);

Calculate

charpoly-eigenvectors-matrix-ratsimp-solve

A:matrix([0,4,0,4],[-...

pol:charpoly(A, t);

ratsimp(pol);

Calculate

charpoly

Run Example
(%i1)m:matrix([1,1,-1],[1,5,1],[1,-1,-2]);
                                [ 1   1   - 1 ]
                                [             ]
(%o1)                           [ 1   5    1  ]
                                [             ]
                                [ 1  - 1  - 2 ]
(%i2) eq1:x+y-z=0;
(%o2)                           - z + y + x = 0
(%i3) eq2:x+5*y+z=0;
(%o3)                           z + 5 y + x = 0
(%i4) eq3:x-y-2*z=0;
(%o4)                          - 2 z - y + x = 0
(%i5) linsolve([eq1,eq2,eq3],[x,y,z]);

solve: dependent equations eliminated: (3)
                             3 %r1        %r1
(%o5)                   [x = -----, y = - ---, z = %r1]
                               2           2
(%i6) n:matrix([3/2],[-(1/2)],[1]);
                                    [  3  ]
                                    [  -  ]
                                    [  2  ]
                                    [     ]
(%o6)                               [   1 ]
                                    [ - - ]
                                    [   2 ]
                                    [     ]
                                    [  1  ]
(%i7) m.n;
                                     [ 0 ]
                                     [   ]
(%o7)                                [ 0 ]
                                     [   ]
                                     [ 0 ]
(%i8) charpoly(m,x);
(%o8)                 ((- x - 2) (5 - x) + 1) (1 - x) + 9
(%i9) 
Run Example
A:matrix([0,1,1],[1,0,1],[1,1,0]);
                                  [ 0  1  1 ]
                                  [         ]
(%o1)                             [ 1  0  1 ]
                                  [         ]
                                  [ 1  1  0 ]
(%i2) expand(charpoly(A,x));
                                   3
(%o2)                           - x  + 3 x + 2
(%i3) 
Run Example
m: matrix ([-2,0,2],[3,-3,0],[8,-6,-2]);
                               [ - 2   0    2  ]
                               [               ]
(%o1)                          [  3   - 3   0  ]
                               [               ]
                               [  8   - 6  - 2 ]
(%i2) Pol: charpoly (m,t);
                                                             2
(%o2)            2 (- 8 (- t - 3) - 18) + (- t - 3) (- t - 2)
(%i3) ratsimp(Pol);
                                     3      2
(%o3)                             - t  - 7 t
(%i4) solve(Pol,t);
(%o4)                          [t = - 7, t = 0]
(%i5) eigenvectors(m);
                                          3    5
(%o5)        [[[- 7, 0], [1, 2]], [[[1, - -, - -]], [[1, 1, 1]]]]
                                          4    2
(%i6) 
[allroots,at,charpoly,float,lambda,matrix,solve] [allroots,at,charpoly,lambda,matrix,solve] [allroots,at,charpoly,lambda,matrix] [at,charpoly,lambda,matrix] [batch,charpoly,determinant,eigenvalues,eigenvectors,ident,invert,load,matrix] [charpoly,coeff,determinant,diagmatrix,ev,matrix,ratexpand,solve,transpose] [charpoly,coeff,determinant,diagmatrix,matrix,ratexpand,solve,transpose] [charpoly,coeff,eliminate,expand,matrix,plot2d,sublis] [charpoly,coeff,eliminate,expand,matrix,sublis] [charpoly,coeff,expand,matrix,solve,sublis] [charpoly,coeff,expand,matrix] [charpoly,coeff,matrix,ratexpand,solve] [charpoly,coeff,matrix,ratexpand] [charpoly,coeff,matrix] [charpoly,determinant,eigenvalues,eigenvectors,ident,invert,load,matrix] [charpoly,determinant,eigenvalues,ident,invert,load,matrix] [charpoly,determinant,eigenvalues,invert,load,matrix] [charpoly,determinant,expand,load,matrix] [charpoly,determinant,invert,matrix] [charpoly,diagmatrix,ev,expand,invert,matrix,transpose] [charpoly,echelon,eigenvalues,eigenvectors,factor,matrix] [charpoly,echelon,eigenvectors,factor,matrix] [charpoly,echelon,eigenvectors,invert,matrix,ratsimp,solve] [charpoly,eigenvalues,eigenvectors,factor,load,matrix,transpose] [charpoly,eigenvalues,eigenvectors,factor,matrix,solve] [charpoly,eigenvalues,eigenvectors,matrix,solve] [charpoly,eigenvalues,eigenvectors,matrix] [charpoly,eigenvalues,expand,gramschmidt,invert,load,matrix,sqrt,transpose] [charpoly,eigenvalues,expand,invert,matrix,solve] [charpoly,eigenvalues,expand,invert,matrix] [charpoly,eigenvalues,expand,load,matrix,sqrt] [charpoly,eigenvalues,expand,matrix] [charpoly,eigenvalues,load,matrix,solve] [charpoly,eigenvalues,matrix] [charpoly,eigenvectors,expand,factor,matrix] [charpoly,eigenvectors,invert,matrix,ratsimp,solve] [charpoly,eigenvectors,matrix,nullspace,rank] [charpoly,eigenvectors,matrix,ratsimp,solve] [charpoly,eigenvectors,matrix] [charpoly,expand,factor,matrix] [charpoly,expand,invert,matrix] [charpoly,expand,lambda,matrix] [charpoly,expand,matrix] [charpoly,factor,load,matrix] [charpoly,factor] [charpoly,matrix,ratsimp,solve] [charpoly,matrix,ratsimp] [charpoly,matrix,solve] [charpoly,matrix] [charpoly]

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