MATRIX EQUATION AXB = E WITH PX = sXP CONSTRAINT

摘要

The matrix equation AXB = E with the constraint PX = sXP is considered, where P is a given Hermitian matrix satisfying P~2 = I and s = ±1. By an eigenvalue decomposition of P, the constrained problem can be equivalently transformed to a well-known unconstrained problem of matrix equation whose coefficient matrices contain the corresponding eigenvector, and hence the constrained problem can be solved in terms of the eigenvectors of P. A simple and eigenvector-free formula of the general solutions to the constrained problem by generalized inverses of the coefficient matrices A and B is presented. Moreover, a similar problem of the matrix equation with generalized constraint is discussed.