Question: 6.21 Mercer's condition. Let X RN be a compact set and K: X X ! R a continuous kernel function. Prove that if

6.21 Mercer's condition. Let X RN be a compact set and K: X X ! R a continuous kernel function. Prove that if K veries Mercer's condition (theorem 6.2), then it is PDS. (Hint: assume that K is not PDS and consider a set fx1; : : : ; xmg X and a column-vector c 2 Rm1 such that Pm i;j=1 cicjK(xi; xj)

< 0.)

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