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May 6, 2011 at 22:55 comment added Gerry Myerson @darij, I'd rather say it can be proved using Hall's Marriage Theorem, or any of a number of other theorems equivalent to Hall's, including one, by Konig, that goes back at least 20 years before Hall, and was stated specifically in the context of matrices.
May 6, 2011 at 19:38 comment added darij grinberg And it's called Hall's marriage theorem.
May 6, 2011 at 7:29 history answered Denis Serre CC BY-SA 3.0