Constrainted least squares solution of Sylvester equation

Abstract

In this paper, we study several constrainted least squares solutions of quaternion Sylvester matrix equation. We first propose a real vector representation of quaternion matrix and study its properties. By using this real vector representation, semi-tensor product of matrices, swap matrix and Moore-Penrose inverse, we derive compatible conditions and the expressions of several constrainted least squares solutions of quaternion Sylvester equation.

Keywords

• quaternion matrix equation
• least squares solution
• semi-tensor product of matrices
• real vector representation
• (anti)η-hermitian matrix