Let's suppose we have a kernel function
In order to prove that this a valid kernel function there are generally two conditions
- It is symmetric
- There exists a map $\varphi:R^d \rightarrow H$ called kernel feature map into some high dimensional feature space $H$ such that $\forall x,x' \ in \ R^d :k(x,x') = \ <\varphi(x),\varphi(x')> $.
How to formally approach to prove these two conditions for this kernel function?