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Math Help - Permutation Matrix

  1. #1
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    Permutation Matrix

    A permutation matrix P is a 0,1-matrix having exactly one 1 in each row and column.
    Prove that a square matrix of nonnegative integers can be expressed as the sum of k permutation matrices if and only if all rows and columns sum to k.

    Can someone show this proof? Thanks a lot!!
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  2. #2
    Member HappyJoe's Avatar
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    Is this still relevant?

    If I recall correctly, there's a proof of this in van Lint and Wilson's book on combinatorics, in the chapter on Hall's theorem.
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