A^-1XA* = A^-1B - A*XB ,两边前乘A,得
XA* = B - AA*XB,因 AA* = |A|E,则
XA* = B - |A|XB
X (A*+ |A|B)= B
X = (A*+ |A|B)^(-1)B,
因 |A* | = |A|^(n-1) ,则 |A| = |A* |^[1/(n-1)],故
X = {A*+ |A*|^[1/(n-1)]B}^(-1)B,
A^-1XA* = A^-1B - A*XB ,两边前乘A,得
XA* = B - AA*XB,因 AA* = |A|E,则
XA* = B - |A|XB
X (A*+ |A|B)= B
X = (A*+ |A|B)^(-1)B,
因 |A* | = |A|^(n-1) ,则 |A| = |A* |^[1/(n-1)],故
X = {A*+ |A*|^[1/(n-1)]B}^(-1)B,