An Exact Solution to a Quaternion Matrix Equation with an Application

Abstract

In this paper, we establish the solvability conditions and the formula of the general solution to a Sylvester-like quaternion matrix equation. As an application, we give some necessary and sufficient conditions for a system of quaternion matrix equations to be consistent, and present an expression of the general solution of the system when it is solvable. We present an algorithm and an example to illustrate the main results of this paper. The findings of this paper generalize the known results in the literature.

Three Symmetrical Systems of Coupled Sylvester-like Quaternion Matrix Equations

“…They presented these findings in terms of the Moore-Penrose inverse of certain given matrices. The resulting equation has wide applications in the linear matrix equations field, see [7,[34][35][36][37][38][39][40]. He and Meng [41] derived the rank equalities solvability conditions for the following quaternion matrix equation with two different restrictions:…”

An Efficient Method for Split Quaternion Matrix Equation X − Af(X)B = C

“…The matrix equation solving problem has important practical value and theoretical significance, which many scholars have been widely concerned by, and which has obtained many valuable results. Liu et al [8] and Mehany et al [9] established the solvability conditions and the formula of the general solution to a Sylvester-like and three symmetrical systems of coupled Sylvester-like quaternion matrix equations, respectively. Ling et al [10] employed matrix LSQR algorithm to deal with quaterniontic least squares problem.…”

The Minimum-Norm Least Squares Solutions to Quaternion Tensor Systems

“…Nowadays, quaternion tensors are often used to solve problems in quantum mechanics, control theory, linear modeling, etc. [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”