B=0 -1 0 0 C=2 1 3 4

题目

B=0 -1 0 0 C=2 1 3 4
0 0 -1 0 0 2 1 3
0 0 0 -1 0 0 2 1
0 0 0 0 0 0 0 2
满足A(E-C^-1B)^TC^T=E+A,求A
(C^-1为C的逆矩阵,（E-C^-1B）^T为括号内矩阵的转置矩阵,C^T为C的转置矩阵)

答案

A(E-C^-1B)^TC^T=A(C(E-C^(-1)))^{T}=A(C-B),所以原式化为A(C^T-B^T-E)=E,即
A=(C^T-B^T-E)^{-1}