Let $A$ be a symmetric positive semi definite matrix, $A \in SPD^n$, and $K \in \mathbb{R}^{k\times k}$ a kernel.
What are the necessary and sufficient conditions over $K$ that will make the convolution of $A$ and $K$ $$ (A * K)_{ij} = \sum_u \sum_v A_{uv}K_{i-u,j-v} $$ Positive semi definite ?
- From the numerical tests I ran, a PSD kernel seems to work. I can't figure out how to prove it though !