### Related

##### eigenvalues-eigenvectors-invert-matrix

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

eigenvalues(A);

eigenvectors(A);

Calculate

##### eigenvalues-eigenvectors-invert-matrix

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

n:matrix([1,0,3],[0,2...

invert (n);

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

A:matrix([-19/6,11/3]...

eigenvectors(A);

eigenvalues(A);

Calculate

##### eigenvalues-eigenvectors-invert-matrix

A:matrix([-19/6,11/3]...

eigenvectors(A);

eigenvalues(A);

Calculate

##### eigenvalues-eigenvectors-invert-matrix

A:matrix([-19/6,11/3]...

eigenvectors(A);

eigenvalues(A);

Calculate

##### eigenvalues-eigenvectors-invert-matrix

f: matrix([0, b1 +p *...

v: matrix([d+v+r1, 0]...

i: invert(v);

Calculate

##### eigenvalues-eigenvectors-invert-matrix

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

eigenvectors(A);

eigenvalues(A);

Calculate

##### eigenvalues-eigenvectors-invert-matrix

A:matrix([-29,-78,-11...

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) ```

### Related Help

Help for Eigenvalues

Help for Eigenvectors

Help for Invert

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