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$B$ is an $n\times m$ matrix, $m\leq n$. I have to find an $n\times n$ positive semidefinite matrix $Y$ such that $YB = 0$. Please help me figure out how can I find the matrix $Y$.

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    How about letting $Y$ be the zero matrix?2011-06-16
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    Yeah. It will be the simplest case, but I need a generalized method.2011-06-16
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    Do you mean you want to find *all* the positive semidefinite matrices $Y$ so that $YB=0$?2011-06-16
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    @mac: No I need not to find all such matrices. But I just want to have at least one n*n Y such that it is positive semidefinite and YB=0 for any given n*m matrix B.2011-06-17
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    @Fatima: should $Y$ be non-zero? (See Gerry's answer). I suggest you add this requirement to the question if that's what you mean.2011-06-17
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    @mac: Y may and may not be zero. Y = 0 is a trivial solution. Anyway, this problem is already solved. Thank you so much for your concern :)2011-06-22

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