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Math Help - Product of Positive Definite Matrices

  1. #1
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    Product of Positive Definite Matrices

    Would someone please show me, or point me to a tutorial on how to prove or disprove that product of positive definite matrices is positive definite.

    Thank you
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  2. #2
    Super Member girdav's Avatar
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    Re: Product of Positive Definite Matrices

    Take A=\begin{pmatrix}2&1\\1&2\end{pmatrix} and B=\begin{pmatrix}3&2\\2&3\end{pmatrix}.
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  3. #3
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    Re: Product of Positive Definite Matrices

    Thanks.
    Is there a proof I could rely on, or is it always proof by example?
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  4. #4
    Super Member girdav's Avatar
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    Re: Product of Positive Definite Matrices

    Sorry, my "counter example" was wrong, since the result is true for matrix of dimension 2. We will have to look at the matrix 3\times 3.
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