Let K1| = AT1C1A1 and K2 = AT2A2 be any two n x n Gram matrices. Let

Question:

Let K1| = AT1C1A1 and K2 = AT2A2 be any two n x n Gram matrices. Let K = K1+ K2.
(a) Show that if K1 + K2 > 0 then K > 0.
(b) Give an example where K1 and K2 are not positive definite, but K > 0.
(c) Show that K = ATCA is also a Gram matrix. Hint: : A will have size (m1 + m2) x n, where mi and m2 are the number of rows in A1, A2, respectively.