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5.48.5 Jordan normal form: jordan

The jordan command finds the Jordan form of a matrix.

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:

jordan([[4,1,1],[1,4,1],[1,1,4]])

Output:




12−1
102
1−2−1



,


600
030
003




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