Minimal Rank Properties of Outer Inverses with Prescribed Range and Null Space

The purpose of this paper is to investigate solvability of systems of constrained matrix equations in the form of constrained minimization problems. The main novelty of this paper is the unification of solutions of considered matrix equations with corresponding minimization problems. For a particular case we extend some well-known results and give several new results for the weak Drazin inverse. The main characterizations of the Drazin inverse, group inverse and Moore-Penrose inverse are obtained as consequences.

Automated summary

The purpose of this paper is to investigate the solvability of systems of constrained matrix equations in the form of constrained minimization problems. The main novelty of this paper is unifying the solutions of the considered matrix equations with the corresponding minimization problems. For a specific case, some well-known results are extended and several new results for the weak Drazin inverse are provided. The main characterizations of the Drazin inverse, group inverse, and Moore-Penrose inverse are obtained as consequences.