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Math Help - rank of matrix

  1. #1
    Junior Member
    Joined
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    rank of matrix

    Prove that
    A be m\times n matrix with rank r iff
    there is an invertible m\times m matrix X and an invertible n\times n matrix Y such that XAY=\begin{pmatrix}I_r & 0\\0 & 0 \end{pmatrix}, where I_r is r\times r identity marix.
    Last edited by KaKa; March 22nd 2009 at 12:28 AM.
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