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Thread: Matrix inequality ( column spaces )

  1. #1
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    Matrix inequality ( column spaces )

    Matrix A is an mxn matrix with rank r and matrix B is a MxN matrix with rank R. The column space of A is in or equal to the column space of B.

    Fill in the inequality ( <= , < , >, = , >= )

    1) m ____ M
    2) r _____ R

    I know that for number two it must be <= but I'm not sure about #1.

    I'm thinking it's = but then I'm doubting it and thinking it might be <=
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  2. #2
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    Re: Matrix inequality ( column spaces )

    I assume you mean: Let $V_A$ be the column space of A and $V_B$ the column space of B with $V_A\subseteq V_B$.

    Thus every column vector of A must be a column vector of B. So it must be that m=M.
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