不是唯一的.
给你个反例:
设 C'AC = diag(4,9)
令 T = diag(1/2,1/3)
则 (TC)'A(CT) = T' (C'AC)T = diag(1/2,1/3)diag(4,9)diag(1/2,1/3)
= diag(1,1).