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Permutation similar matrices

asked 2017-02-15 12:18:48 -0600

Deepak Sarma gravatar image

How to generate the class of all permutation similar matrices of a given square matrix?

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fidbc gravatar imagefidbc ( 2017-02-20 13:38:38 -0600 )edit

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answered 2017-02-16 02:37:43 -0600

Sébastien gravatar image
sage: M = random_matrix(ZZ,3,3)
sage: M
[-2  0 -6]
[ 0  1  3]
[ 0  3  1]
sage: P = [matrix(p) for p in Permutations(3)]
sage: similar = [p*M*~p for p in P]
sage: similar
[
[-2  0 -6]  [-2 -6  0]  [ 1  0  3]  [ 1  0  3]  [ 1  3  0]  [ 1  3  0]
[ 0  1  3]  [ 0  1  3]  [ 0 -2 -6]  [-6 -2  0]  [ 3  1  0]  [ 3  1  0]
[ 0  3  1], [ 0  3  1], [ 3  0  1], [ 3  0  1], [ 0 -6 -2], [-6  0 -2]
]
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Asked: 2017-02-15 12:18:48 -0600

Seen: 122 times

Last updated: Feb 16