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I have a simple question relating to permutation matrices.

We have an a matrix, X. We have a permutation matrix, P. We can get the permuted version of X by doing

permutedX = P*X*P'.

Now, I want to represent the matrices in vector form. The way the books mention it as follows.

They define vectors p = vec(P) by putting each row of P one after the other. Then constructing Y = p*transpose(p). So, P is of size n by n and Y is of size n^2 by n^2. they then construct vec(X) and define a matrix M of size n^2 by n^2 by putting elements of vec(X) on its main diagonal. The following statement confuses me.

M*Y is equivalent to the first equation,

I tried doing this in matlab considering P to be a simple identity matrix of size 3 by 3. does not work. i am possibly missing something really simple. can somebody tell me how this reasoning works.

thanks.

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# Permutation matrices in vector form

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