Consimilarity of Split Quaternion Matrices and a Solution of the Split Quaternion Matrix Equation X-AX_B=C

TL;DR

This paper extends the concept of consimilarity from complex matrices to split quaternion matrices, introduces coneigenvalues and coneigenvectors for these matrices, and provides explicit solutions for a specific matrix equation.

Contribution

It generalizes consimilarity to split quaternion matrices, defines coneigenvalues and coneigenvectors, and characterizes solutions to the matrix equation X-AXB=C.

Findings

Established the concept of coneigenvalues and coneigenvectors for split quaternion matrices.

Characterized the existence of solutions to X-AXB=C.

Derived explicit solutions using real representations.

Abstract

In this paper, the consimilarity of complex matrices is generalized for the split quaternions. In this regard, coneigenvalue and coneigenvector are defined for split quaternion matrices. Also, the existence of solution to the split quaternion matrix equation X-AXB = C is characterized and the solution of the equation in the explicit form are derived via its real representation.