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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Take $\displaystyle A=\begin{pmatrix}2&1\\1&2\end{pmatrix}$ and $\displaystyle B=\begin{pmatrix}3&2\\2&3\end{pmatrix}$.
Thanks. Is there a proof I could rely on, or is it always proof by example?
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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