# Product of Positive Definite Matrices

• Oct 1st 2011, 05:54 AM
itpro
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
• Oct 1st 2011, 05:58 AM
girdav
Re: Product of Positive Definite Matrices
Take $A=\begin{pmatrix}2&1\\1&2\end{pmatrix}$ and $B=\begin{pmatrix}3&2\\2&3\end{pmatrix}$.
• Oct 1st 2011, 06:28 AM
itpro
Re: 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 AM
girdav
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 $3\times 3$.