Solvability of the matrix inequality

Abstract

In this paper, we first investigate the matrix equation in a new fashion, where A, B, C, D and G are arbitrary matrices. Then, we establish some necessary and sufficient conditions for the existence of a solution of , where A, B are arbitrary matrices and C is a Hermitian matrix. In the special case when , we determine the general solution of , where A is an arbitrary matrix and C is a Hermitian matrix.

Keywords:

• Matrix equation
• matrix inequality
• Löwner partial ordering
• generalized inverse

AMS Subject Classifications:

• 15A24
• 15A09
• 15B57

Acknowledgements

The authors would like to sincerely thank the references for several valuable comments in improving the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.