The matrix equation with or constraint is considered, where S, R are Hermitian idempotent, P, Q are Hermitian involutory, and . By the eigenvalue decompositions of S, R, the equation with constraint is equivalently transformed to an unconstrained problem whose coefficient matrices contain the corresponding eigenvectors, with which the constrained solutions are constructed. The involved eigenvectors are released by Moore-Penrose generalized inverses, and the eigenvector-free formulas of the general solutions are presented. By choosing suitable matrices S, R, we also present the eigenvector-free formulas of the general solutions to the matrix equation with constraint.
"Eigenvector-Free Solutions to the Matrix Equation with Two Special Constraints." J. Appl. Math. 2013 1 - 7, 2013. https://doi.org/10.1155/2013/869705