3.6 If f(s)is an arbitrary finite real-valued function ofs d, show that ????(s, t) = f(s)f(t) is positive semidefinite. Hint: For coefficients a1, ...,

3.6 If f(s)is an arbitrary finite real-valued function ofs ∈ ℝd, show that ????(s, t) =

f(s)f(t) is positive semidefinite.

Hint: For coefficients a1, ..., an and sites t1, ..., tn note the identity

∑ ai aj f(ti

)f(tj

)={∑ ai f(ti

)}2 ≥ 0.