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I am looking for the name of the next simple fact(theorem):

let $M$ be some matrix and let $k$ be some combinatorial rectangle in $M$. denote the matrix of $k$ by $M_k$. It holds that:

$Rank(M)\ge Rank(M_k)$

(I can easily prove it. But I want my paper to be brief so I just want to quote this theorem in the paper).

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1 Answer 1

up vote 2 down vote accepted

I'm not sure this result has a name, but Meyer in his Matrix Analysis and Applied Linear Algebra states the Rank and the Largest Nonsingular Submatrix theorem, from which your result follows easily. See Section 4.5, page 215.

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thank you, found it. –  zvisofer Nov 13 '12 at 21:52

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