Research on Least‐Square η‐Hermitian Solutions of Split Quaternion Matrix Equations

Abstract

In this article, we use the real representation matrix of the split quaternion matrix, vector operator, Kronecker product, and Moore–Penrose generalized inverse. We establish the least norm expression of the least‐square η‐Hermitian solution and the least norm expression of the least‐square η‐anti‐Hermitian solution on the split quaternion of the matrix equation AXB + CXD = E. The final solution expression is represented only by real matrices and real vectors. In the algorithm, only real number operations are involved, which avoids complex quaternion operations and greatly reduces the amount of computation. Finally, we use two examples to verify the effectiveness of the proposed algorithm.