Sponsored links: Algebra eBooks
 

Related

eigenvectors-matrix

eigenvectors(matrix([...

Calculate

eigenvectors-matrix

t0:matrix([1,1/4,0],[...

eigenvectors(t0);

v:matrix([1],[-2],[1]);

Calculate

eigenvectors-matrix

a:matrix([-4,0,-2],[0...

eigenvectors(a);

Calculate

eigenvectors-matrix-ratsimp-sqrt-transpose

H: matrix([E1, g], [g...

J: eigenvectors(H);

v: J[2][1][1];

Calculate

eigenvectors-matrix

A:matrix([3,-1,1],[7,...

eigenvectors(A);

Calculate

eigenvectors-matrix

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

eigenvectors(A);

Calculate

eigenvectors-matrix

a:matrix([1,3,-3],[2,...

eigenvectors(a);

Calculate

eigenvectors-matrix

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

evA:eigenvectors(A);

Calculate

eigenvectors-matrix

M:matrix([1,2,3],[4,5...

eigenvectors(M);

Calculate

eigenvectors-float-matrix

A:matrix([1,0.5,3],[2...

[W,a]:eigenvectors(A);

float(W);

Calculate

eigenvectors

Run Example
(%i1)load(eigen);
(%o1)           /usr/share/maxima/5.21.1/share/matrix/eigen.mac
(%i2) P: matrix([0,1,0],[0,0,1],[1,0,0]);
                                  [ 0  1  0 ]
                                  [         ]
(%o2)                             [ 0  0  1 ]
                                  [         ]
                                  [ 1  0  0 ]
(%i3) Pdag: ctranspose(P);
                                  [ 0  0  1 ]
                                  [         ]
(%o3)                             [ 1  0  0 ]
                                  [         ]
                                  [ 0  1  0 ]
(%i4) A: P+Pdag;
                                  [ 0  1  1 ]
                                  [         ]
(%o4)                             [ 1  0  1 ]
                                  [         ]
                                  [ 1  1  0 ]
(%i5) hermitianmatrix: false;
(%o5)                                false
(%i6) [L, V]: eigenvectors(A);
(%o6)   [[[2, - 1], [1, 2]], [[[1, 1, 1]], [[1, 0, - 1], [0, 1, - 1]]]]
(%i7) Ltmp: [];
(%o7)                                 []
(%i8) Vtmp: [];
(%o8)                                 []
(%i9) for i:1 thru length(L[1]) do    for j:1 thru L[2][i] do      (        Ltmp: append(Ltmp, [L[1][i]]),     Vtmp: append(Vtmp, V[i][j])  );
(%o9)                                done
(%i10) Ltmp;
(%o10)                           [2, - 1, - 1]
(%i11) Vtmp;
(%o11)                  [1, 1, 1, 1, 0, - 1, 0, 1, - 1]
(%i12) U: tranpose(matrix(Vtmp));
(%o12)            tranpose([ 1  1  1  1  0  - 1  0  1  - 1 ])
(%i13) D: apply(diag_matrix, Ltmp);
                                [ 2   0    0  ]
                                [             ]
(%o13)                          [ 0  - 1   0  ]
                                [             ]
                                [ 0   0   - 1 ]
(%i14) 
Run Example
I: matrix([1,0],[0,1]);
                                   [ 1  0 ]
(%o1)                              [      ]
                                   [ 0  1 ]
(%i2) S_z: matrix([1,0],[0,-1]);
                                  [ 1   0  ]
(%o2)                             [        ]
                                  [ 0  - 1 ]
(%i3) S_x: matrix([0,1],[1,0]);
                                   [ 0  1 ]
(%o3)                              [      ]
                                   [ 1  0 ]
(%i4) S_y: matrix([0,-%i],[%i,0]);
                                 [ 0   - %i ]
(%o4)                            [          ]
                                 [ %i   0   ]
(%i5) [vals,vecs]:eigenvectors(kronecker_product(S_x,S_y));
(%o5) [[[- 1, 1], [2, 2]], [[[1, 0, 0, - %i], [0, 1, %i, 0]], 
                                             [[1, 0, 0, %i], [0, 1, - %i, 0]]]]
(%i6) 
Run Example
A:matrix([1,2],[2,1]);
                                   [ 1  2 ]
(%o1)                              [      ]
                                   [ 2  1 ]
(%i2) eigenvalues(A);
(%o2)                         [[3, - 1], [1, 1]]
(%i3) eigenvectors(A);
(%o3)            [[[3, - 1], [1, 1]], [[[1, 1]], [[1, - 1]]]]
(%i4) 
[adjoint,determinant,eigenvalues,eigenvectors,invert,matrix] [append,apply,ctranspose,do,eigenvectors,false,load,matrix] [append,apply,ctranspose,eigenvectors,false,load,matrix] [batch,charpoly,determinant,eigenvalues,eigenvectors,ident,invert,load,matrix] [bfloat,eigenvectors,load,matrix] [bfloat,eigenvectors,matrix] [charpoly,determinant,eigenvalues,eigenvectors,ident,invert,load,matrix] [charpoly,echelon,eigenvectors,factor,matrix] [charpoly,echelon,eigenvectors,invert,matrix,ratsimp,solve] [charpoly,eigenvalues,eigenvectors,matrix] [charpoly,eigenvectors,invert,matrix,ratsimp,solve] [charpoly,eigenvectors,matrix,nullspace,rank] [charpoly,eigenvectors,matrix,ratsimp,solve] [charpoly,eigenvectors,matrix] [cos,eigenvalues,eigenvectors,invert,matrix,sin] [cos,eigenvectors,matrix,sin] [ctranspose,eigenvectors,matrix] [determinant,eigenvalues,eigenvectors,ident,invert,matrix,rank,submatrix,transpose] [determinant,eigenvalues,eigenvectors,ident,load,matrix,ratsimp,solve,sqrt,transpose] [determinant,eigenvalues,eigenvectors,matrix] [determinant,eigenvectors,expand,hessian] [determinant,eigenvectors,matrix] [diag_matrix,eigenvectors,matrix,transpose] [eigenvalues,eigenvectors,factor,matrix] [eigenvalues,eigenvectors,float,floor,matrix] [eigenvalues,eigenvectors,float,matrix] [eigenvalues,eigenvectors,invert,matrix] [eigenvalues,eigenvectors,load,matrix,ratsimp,sqrt,transpose] [eigenvalues,eigenvectors,load,matrix,sqrt,transpose] [eigenvalues,eigenvectors,load,matrix,sqrt] [eigenvalues,eigenvectors,load,matrix] [eigenvalues,eigenvectors,matrix,permanent] [eigenvalues,eigenvectors,matrix] [eigenvectors,expand,hessian] [eigenvectors,float,matrix] [eigenvectors,hessian,load] [eigenvectors,ident,matrix,nullity,nullspace] [eigenvectors,ident,matrix,nullity] [eigenvectors,ident,matrix,sqrt,transpose] [eigenvectors,ident,matrix,transpose] [eigenvectors,invert,matrix,sqrt] [eigenvectors,invert,matrix,transpose] [eigenvectors,invert,matrix] [eigenvectors,is,matrix,ratsimp,sqrt,tex,transpose] [eigenvectors,load,matrix] [eigenvectors,matrix,solve] [eigenvectors,matrix,sqrt] [eigenvectors,matrix,transpose] [eigenvectors,matrix,triangularize] [eigenvectors,matrix]

Related Help

Help for Eigenvectors