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eigenvalues-eigenvectors-invert-matrix

A:matrix([-19/6,22/6]...

eigenvalues(A);

eigenvectors(A);

Calculate

eigenvalues-eigenvectors-invert-matrix

A: matrix ([-19/6, 22...

eigenvalues (A);

eigenvectors (A);

Calculate

eigenvalues-eigenvectors-invert-matrix

A:matrix([-19/6,22/6]...

eigenvectors(A);

eigenvalues(A);

Calculate

eigenvalues-eigenvectors-invert-matrix

m: matrix ([1,-3,3],[...

eigenvalues (m);

eigenvectors (m);

Calculate

eigenvalues-eigenvectors-invert-matrix

A: matrix ([-19/6, 22...

eigenvalues (A);

eigenvectors (A);

Calculate

eigenvalues-eigenvectors-invert-matrix

A:matrix([-19/6,22/6]...

eigenvalues(A);

eigenvectors(A);

Calculate

eigenvalues-eigenvectors-invert-matrix

A:matrix([-19/6,22/6]...

eigenvalues(A);

eigenvectors(A);

Calculate

eigenvalues-eigenvectors-invert-matrix

A:matrix([-19/6,22/6]...

eigenvalues(A);

eigenvectors(A);

Calculate

eigenvalues-eigenvectors-invert-matrix

m: matrix ([1,1,1],[0...

u: matrix ([1,0,3],[0...

eigenvalues (m);

Calculate

eigenvalues-eigenvectors-invert-matrix

A:matrix([-19/6,22/6]...

eigenvalues(A);

eigenvectors(A);

Calculate

[eigenvalues,eigenvectors,invert,matrix]

Run Example
(%i1)A:matrix([-19/6,22/6],[11/6,-8/6]);
                                 [   19  11  ]
                                 [ - --  --  ]
                                 [   6   3   ]
(%o1)                            [           ]
                                 [  11     4 ]
                                 [  --   - - ]
                                 [  6      3 ]
(%i2) eigenvalues(A);
                                     1
(%o2)                         [[- 5, -], [1, 1]]
                                     2
(%i3) eigenvectors(A);
                         1                    1
(%o3)            [[[- 5, -], [1, 1]], [[[1, - -]], [[1, 1]]]]
                         2                    2
(%i4) matrixproduct(A,invert(A));
                                 [   19  11  ]  [ 8   22 ]
                                 [ - --  --  ]  [ --  -- ]
                                 [   6   3   ]  [ 15  15 ]
(%o4)              matrixproduct([           ], [        ])
                                 [  11     4 ]  [ 11  19 ]
                                 [  --   - - ]  [ --  -- ]
                                 [  6      3 ]  [ 15  15 ]
(%i5) 
Run Example
A:matrix([1,a],[a,1]);
                                   [ 1  a ]
(%o1)                              [      ]
                                   [ a  1 ]
(%i2) eigenvalues(A);
(%o2)                      [[1 - a, a + 1], [1, 1]]
(%i3) invert(A);
                            [    1          a    ]
                            [  ------   - ------ ]
                            [       2          2 ]
                            [  1 - a      1 - a  ]
(%o3)                       [                    ]
                            [     a        1     ]
                            [ - ------   ------  ]
                            [        2        2  ]
                            [   1 - a    1 - a   ]
(%i4) eigenvectors(A);
(%o4)         [[[1 - a, a + 1], [1, 1]], [[[1, - 1]], [[1, 1]]]]
(%i5) 
Run Example
A:matrix([-19/6,22/6],[11/6,-8/6]);
                                 [   19  11  ]
                                 [ - --  --  ]
                                 [   6   3   ]
(%o1)                            [           ]
                                 [  11     4 ]
                                 [  --   - - ]
                                 [  6      3 ]
(%i2) eigenvalues(A);
                                     1
(%o2)                         [[- 5, -], [1, 1]]
                                     2
(%i3) eigenvectors(A);
                         1                    1
(%o3)            [[[- 5, -], [1, 1]], [[[1, - -]], [[1, 1]]]]
                         2                    2
(%i4) T:matrix([1,-1/2],[1,1]);
                                  [      1 ]
                                  [ 1  - - ]
(%o4)                             [      2 ]
                                  [        ]
                                  [ 1   1  ]
(%i5) invert(T);
                                  [  2   1 ]
                                  [  -   - ]
                                  [  3   3 ]
(%o5)                             [        ]
                                  [   2  2 ]
                                  [ - -  - ]
                                  [   3  3 ]
(%i6) invert(T).T.A;
                                 [   19  11  ]
                                 [ - --  --  ]
                                 [   6   3   ]
(%o6)                            [           ]
                                 [  11     4 ]
                                 [  --   - - ]
                                 [  6      3 ]
(%i7) 
[abs,carg,float,invert,matrix,polarform,ratsimp,rectform] [addcol,addrow,diff,do,ev,genmatrix,invert,kill,load,matrix,plot2d,romberg,sqrt,submatrix] [addcol,addrow,diff,ev,genmatrix,invert,kill,length,lmax,lmin,load,matrix,plot2d,romberg,sqrt,submatrix] [adjoint,determinant,invert,matrix] [at,eigenvalues,invert,jacobian] [charpoly,determinant,eigenvalues,eigenvectors,ident,invert,load,matrix] [charpoly,echelon,eigenvectors,invert,matrix,ratsimp,solve] [cos,eigenvalues,invert,matrix,numer,sin,transpose,true] [cos,invert,matrix,numer,sin,transpose,true] [cos,invert,matrix,sin] [determinant,diagmatrix,eigenvectors,invert,matrix,modulus,solve,transpose,triangularize] [determinant,eigenvalues,eigenvectors,ident,invert,matrix,rank,submatrix,transpose] [determinant,eigenvalues,eigenvectors,ident,load,matrix,ratsimp,solve,sqrt,transpose] [determinant,eigenvalues,ident,invert,matrix,rank,submatrix,transpose] [determinant,eigenvalues,invert,lambda,matrix,radcan,solve,sqrt] [determinant,invert,matrix,transpose] [determinant,invert,matrix] [eigenvalues,eigenvectors,float,floor,matrix] [eigenvalues,eigenvectors,float,matrix] [eigenvalues,eigenvectors,invert,matrix] [eigenvalues,eigenvectors,lambda,matrix] [eigenvalues,eigenvectors,load,matrix,ratsimp,sqrt,transpose] [eigenvalues,eigenvectors,load,matrix,sqrt,transpose] [eigenvalues,eigenvectors,load,matrix,sqrt] [eigenvalues,eigenvectors,matrix] [eigenvalues,ev,matrix,ratsimp,solve,sqrt] [eigenvalues,float,matrix] [eigenvalues,invert,jacobian,matrix] [eigenvalues,invert,matrix,numer,transpose,true] [eigenvalues,invert,matrix,transpose] [eigenvalues,invert,matrix] [eigenvalues,matrix,transpose] [eigenvalues,matrix] [eigenvectors,invert,matrix,sqrt] [eigenvectors,invert,matrix] [eigenvectors,load,matrix] [eigenvectors,matrix,transpose] [eigenvectors,matrix] [factor,ident,invert,matrix] [factor,invert,matrix] [float,invert,matrix,transpose] [float,invert,matrix] [invert,kill,matrix,transpose] [invert,load,matrix] [invert,matrix,phi,transpose] [invert,matrix,rank,transpose] [invert,matrix,ratsimp] [invert,matrix,sqrt] [invert,matrix,transpose] [invert,matrix]

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