試題詳解

15. (10%) For _n > 1, let S_n denote the set of all symmetric matrices and T_n denote the set of all skew-symmetric matrices, that is, T_n = {A | A is a n x n matrix such that A^T = -A}. Let U be a n x n matrix such that U^TU = I_n. Furthermore, let
 Wu ={M I M is a n x n matrix such that U^TMU is a diagonal matrix}.
For a n xn matrix A, let Au denote the unique matrix B in Wu such that is minimized. Choose the correct statement(s) from the following.
 
(A) S_n is a subspace of and its dimension is n.
(B) T. is a subspace of  and its dimension is n.
(C) W_U is a subspace of and its dimension is n.
(D)
(E)