The least squares Bisymmetric solution of quaternion matrix equation AXB=C

Abstract

In this paper, the idea of partitioning is used to solve quaternion least squares problem, we divide the quaternion Bisymmetric matrix into four blocks and study the relationship between the block matrices. Applying this relation, the real representation of quaternion, and M-P inverse, we obtain the least squares Bisymmetric solution of quaternion matrix equation AXB=C and its compatable conditions. Finally, we verify the effectiveness of the method through numerical examples.

Keywords

• block matrix
• bisymmetric matrix
• quaternion matrix equation
• least squares solution
• real representation