Question: P75. (2p) Let A E Rnxn be s.p.d., q(A) be any polynomial of A, and { v1, . . ., Vn} the orthonormal eigenbasis of

P75. (2p) Let A E Rnxn be s.p.d., q(A) be any polynomial of A, and { v1, . . ., Vn} the orthonormal eigenbasis of A, i.e. Avi = liVi and V vi = dij Show that (a) 1bll3 - ELIAi(b vi)2 for any b ER". (b) 1/q(A)bll2 = En, dig()i)?(b vi)2 for any be Rn

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