Four symmetric systems of the matrix equations with an application over the Hamilton quaternions

Abstract

In this paper, we established some necessary and sufficient conditions for the four symmetric systems to be consistent. Moreover, we derived the expressions of their general solutions when they were solvable. As an application, we investigated the solvability conditions of matrix equations involving $ \eta $-Hermicity matrices. Finally, we presented an example to illustrate the main results of this paper.

Keywords

• matrix equation
• quaternion
• moore-penrose
• rank
• $ \eta $-hermitian matrix