Optimization Problems of the Rank and Inertia Corresponding to a Hermitian Least-Squares Problem

摘要

Generally, the least-squares problem can be solved by the normal equation. Based on the projection theorem, we propose a direct method to investigate the maximal and minimal ranks and inertias of the least-squares solutions of matrix equation AXB= C under Hermitian constraint, and the corresponding formulas for calculating the rank and inertia are derived.