Direct methods onη‐Hermitian solutions of the split quaternion matrix equation (AXB,CXD)=(E,F)
Ming‐Zhao Li, S. J. Yuan, Hua Bing Jiang · Mathematical Methods in the Applied Sciences · 2021
This paper provides two direct methods for solving the split quaternion matrix equation whereXis an unknown split quaternionη‐Hermitian matrix, andA, B, C, D, E, Fare known split quaternion matrices with suitable size. Our tools are the Kronecker product, Moore–Penrose generalized inverse, real representation, and complex representation of split quaternion matrices. Our main work is to find the necessary and sufficient conditions for the existence of a solution of the matrix equation mentioned above, derive the explicit solution representation, and provide four numerical algorithms and two numerical examples.