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Is it possible to decompose a matrix A having n rows and n columns to sum of m [n x n] permutation matrices. where m is the number of 1’s in each row and each column in matrix A?
UPDATE:
yes, this is possible. I came across such an exmaple which is shown below – but How can we generalize the answer?
What you want is called a 1-factorization. One algorithm is repeatedly to find a perfect matching and remove it; probably there are others.