The Least Square Solution with the Least Norm to a System of Quaternion Matrix Equations

We in this paper derive the expression of the least square solution with the least norm to the system of generalized Sylvester quaternion matrix equations A1X=E1,XB1=E2,C1Y=E3,YD1=E4,A2XB2+C2YD2=E5,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} A_1X = E_1 ,\quad XB_1 = E_2, \quad C_1Y = E_3 ,\quad YD_1 = E_4,\quad A_2XB_2+C_2YD_2=E_5, \end{aligned}$$\end{document}where X, Y are unknown quaternion matrices and the others are given quaternion matrices.