問題詳情

15. (10%) For n > 1, let Sn denote the set of all symmetric matrices and Tn denote the set of allskew-symmetric matrices, that is, Tn = {A | A is a n x n matrix such that AT = -A}. Let Ube a n x n matrix such that UTU = In. Furthermore, let
 Wu ={M I M is a n x n matrix such that UTMU 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) Sn is a subspace of

and its dimension is n.
(B) T. is a subspace of 

 and its dimension is n.
(C) WU is a subspace of

 and its dimension is n.
(D)


(E)

參考答案