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Thread: 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 $\displaystyle A=\begin{pmatrix}2&1\\1&2\end{pmatrix}$ and $\displaystyle B=\begin{pmatrix}3&2\\2&3\end{pmatrix}$.
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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 $\displaystyle 3\times 3$.
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