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Exercise 9.6.6. Consider maximizing h() in (9.36) over $ 6 S,. (a) Let 4 = TAT' be the spectral decomposition of T, so that the diagonals of A are the eigenvalues M1 2 12 2 ... 2 A 20. (Recall Theorem 1.1.) Show that - trace(* ) = [A-9/2 2-1/(2A.)]. (9.104) i=1 (b) Find Mi, the maximizer of A /Zexp(-1/(2);)), for each i = 1,...,q. (c) Show that these A/'s satisfy the conditions on the eigenvalues of A. (d) Argue that then 4 = (1/a)I, maximizes h(Y). 8(2) = h(U-1/2EU-1/2), where (Y) = U|4/2 Y#/2 e ? trace (Y-1) (9.36) 2. [10 pts] Exercise 9.6.6. Note: a > 0, and you should actually be maximizing over De S. so that A1 2 12 2 .. . > > >0. Use the note and equation 9.36 on the right to answer exercise 9.6.6