THE EXTREMAL RANKS AND INERTIAS OF THE LEAST SQUARES SOLUTIONS TO MATRIX EQUATION AX = B SUBJECT TO HERMITIAN CONSTRAINT
Lifang Dai, Maolin Liang · Journal of applied mathematics & informatics · 2013
In this paper, the formulas for calculating the extremal ranks and inertias of the Hermitian least squares solutions to matrix equation AX = B are established. In particular, the necessary and sufficient conditions for the existences of the positive and nonnegative definite solutions to this matrix equation are given. Meanwhile, the least squares problem of the above matrix equation with Hermitian R-symmetric and R-skew symmetric constraints are also investigated.