# Math Help - Product of Positive Definite Matrices

1. ## 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

2. ## Re: Product of Positive Definite Matrices

Take $A=\begin{pmatrix}2&1\\1&2\end{pmatrix}$ and $B=\begin{pmatrix}3&2\\2&3\end{pmatrix}$.

3. ## Re: Product of Positive Definite Matrices

Thanks.
Is there a proof I could rely on, or is it always proof by example?

4. ## 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 $3\times 3$.