- #1
vix_cse
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hi all
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.
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.