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5.48.4  Rational Jordan matrix: rat_jordan

The rat_jordan command finds the rational Jordan form of a matrix.

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:

rat_jordan([[4,1,1],[1,4,1],[1,1,4]])

Output:




12−1
102
1−2−1



,


600
030
003




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