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Math Help - Matrix algebra problem: when C=(A-1 - B-1) will have all diagonals > 0

  1. #1
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    Matrix algebra problem: when C=(A-1 - B-1) will have all diagonals > 0

    I need a proof of the following:
    If A and B are real, symmetric, positive definite matrices having
    All diagonal elements positive.
    At what circumstances C = (A-1 B-1) has all diagonal element positive.
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  2. #2
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    Re: Matrix algebra problem: when C=(A-1 - B-1) will have all diagonals > 0

    I don't understand your notation. What does A-1 or B-1 mean?
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  3. #3
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    Re: Matrix algebra problem: when C=(A-1 - B-1) will have all diagonals > 0

    My apologies. A-1 mean inverse of A. Similar for B.
    I have two co-variance matrices A and B. I invert them and take the difference between A and B.
    I want to know at what conditions the difference matrix C = (A(inv) - B(inv)) will have all diagonal elements > 0.
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