The jordan command finds the Jordan form of a matrix.
J=P−1AP |
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 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:
⎡ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎦ | , | ⎡ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎦ |