Hence there's some permutation of $A$ that does not appear in our list of all $RAC$ matrices.īTW, just to close this out: for $1 \times 1$ matrices, the answer is "yes, all permutations can in fact be realized by row and column permutations." I suspect you knew that. So the number of possible results of applying row- and col-permutations to $A$ is smaller than the number of possible permutations of the elements of $A$. The Dulmage-Mendelsohn decomposition (dmperm in MATLAB) can be used to do this for symmetric matrices (or just turn your non-symmetric matrix into a matrix of 0's and 1's with 1's replacing all non-zero entries in the original matrix. ![]()
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