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Math Help - equation system on the diagonals of matrix product

  1. #1
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    equation system on the diagonals of matrix product

    I'm looking for the set of m*n matrices W that simultaneously solve:
    diag(AW)=b and diag(WA)=c for a given n*m matrix A and vectors b and c. With diag() I mean the vector of diagonal elements.
    I'm happy even for just a starting point, or a single solution.
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  2. #2
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    Re: equation system on the diagonals of matrix product

    Unless m = n = 2, your dealing with an under-determined system aren't you ?
    The first equation diag(AW) = b gets you n linear equations and the second, diag(WA) = c, m linear equations in the elements of W.
    That means m + n equations for the mn unknown elements of W.
    If that's the case ? there will be mn - m - n free variables.
    Decide where, in W, you want these to be and solve for the others in terms of them.
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  3. #3
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    Re: equation system on the diagonals of matrix product

    Thanks for that. I was first thinking to somehow capture the full space of solutions. But on second thought I can come of with some reasonable set of constraints to narrow down the problem, hopefully to a single solution.
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