Suppose we have n kernel functions Kj(,), j = 1, ..., n such that there are n implicit high-dimensional feature maps ; : Rd RD RD j = 1, ... , n that satisfies Vx, z E Rd, Kj(x, z) = (; (x), j(z)), where (0;(x), j(z)) = , (x); (z); is the dot product (a.k.a. inner product) in the D-dimensional space. (.) i=1 denotes the i-th dimension of the j-th mapped feature. j Is the summation of those kernel functions, that is, K(x, z) = ; K;(x, z), still a valid kernel function? If yes, prove that. If no, please explain why (You can attach images for your derivation)