Prove that ${f(x,y) = x^Txx^Tyy^Ty}$ is a valid kernel The rules I can use without a proof are the following ones:

The thing that I know that a kernel is valid if it is symmetric, e.g. ${f(x,y) = f(y,x)}$ and if ${c^TKc >= 0}$, for each vector ${c \neq 0}$, but I don't know how to prove it, and don't know how to get the matrix K (if this is the correct way to solve this exercise).

I think you can use R3 and get $xx^Tyy^T $and then mention that is $x^2y^2$
