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From: "Bruno Luong" <b.luong@fogale.findmycountry>
Newsgroups: comp.soft-sys.matlab
Subject: Re: finding permutation matrices using eig()
Date: Fri, 23 Apr 2010 06:14:07 +0000 (UTC)
Organization: FOGALE nanotech
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"Leslie Watkins" <Theantipoke@gmail.com> wrote in message <hqrck0$pl8$1@fred.mathworks.com>...
> I have two matrices A and B:
> A = [0 1 1 1 0; 1 0 1 0 0; 1 1 0 1 1; 1 0 1 0 0; 0 0 1 0 0]
> B = [0 1 1 1 0; 1 0 1 0 0; 1 1 0 1 1; 1 0 1 0 1; 0 0 1 1 0]
> There exists a permutation matrix P such that P*A*P' = B.
> (P = [0 0 1 0 0;  0 0 0 1 0; 1 0 0 0 0; 0 0 0 0 1; 0 1 0 0 0])
 

Stop right there, it's not correct.

When we multiply (left or right) by a permutation matrix, the elements only change places. In particular the number "1s" should remain identical.

But B has 2 more 1s than A (14 vs 12), so B can not be permutation of A as you have stated.

The statement is wrong not only for the P you provide but any permutation matrix P.

Bruno