The rat_jordan command finds the rational Jordan form of a matrix.
J=P−1AP |
rat_jordan(A) (in Maple mode) only returns the matrix J.
Examples.
⎡ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎦ | , | ⎡ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎦ |
⎡ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎦ |
⎡ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎦ |
⎡ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎦ | , | ⎡ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎦ |
⎡ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎦ | , | ⎡ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎦ |
If A is symmetric and has eigenvalues with multiple orders, the matrix P returned by rat_jordan(A) will contain orthogonal eigenvectors (not always of norm equal to 1); i.e., tran(P)*P will be a diagonal matrix where the diagonal is the square norm of the eigenvectors.
Example.
Input:
Output:
⎡ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎦ | , | ⎡ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎦ |