I need to show that hadamard (schur) product $ A \circ B$ can be positive definite even if not both A and B are positive definite. It would be nice to see a simple example which prooves this.
I know that According to Schur Product Theorem, if both A and B are positive definite, then their hadamard (schur) product $ A \circ B$ is also positive definite.
Consider the $1\times1$ matrices $A=(-1)$ and $B=(-1)$.