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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- Oct 1st 2011, 05:54 AMitproProduct 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 - Oct 1st 2011, 05:58 AMgirdavRe: Product of Positive Definite Matrices
Take $\displaystyle A=\begin{pmatrix}2&1\\1&2\end{pmatrix}$ and $\displaystyle B=\begin{pmatrix}3&2\\2&3\end{pmatrix}$.

- Oct 1st 2011, 06:28 AMitproRe: Product of Positive Definite Matrices
Thanks.

Is there a proof I could rely on, or is it always proof by example? - Oct 1st 2011, 07:04 AMgirdavRe: 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 $\displaystyle 3\times 3$.