Exercise 31.1.3 Let C [ i j ] be a positive definite matrix. (1) Prove that

Exercise 31.1.3 Let C ≡ [ σi j ] be a positive definite matrix. (1) Prove that maxi σii is the maximum value of

i

j ωiωjσi j under the constraints

i ωi = 1 and ωi ≥ 0.

(2) How about the minimum value under the same constraints? (You may assume that the row sums of C−1 are all nonnegative.)