Computational methods for linear matrix equations

V Simoncini - siam REVIEW, 2016‏ - SIAM
Given the square matrices A,B,D,E and the matrix C of conforming dimensions, we consider
the linear matrix equation A\mathbfXE+D\mathbfXB=C in the unknown matrix \mathbfX. Our …

A new Sylvester-type quaternion matrix equation model for color image data transmission

ZH He, WL Qin, J Tian, XX Wang, Y Zhang - Computational and Applied …, 2024‏ - Springer
In this paper, we investigate an encryption method for color image data transmission based
on Sylvester-type quaternion matrix equations. We first study the solvability conditions and …

A system of quaternary coupled Sylvester-type real quaternion matrix equations

ZH He, QW Wang, Y Zhang - Automatica, 2018‏ - Elsevier
In this paper we establish some necessary and sufficient solvability conditions for a system
of quaternary coupled Sylvester-type real quaternion matrix equations in terms of ranks and …

Investigation of some Sylvester-type quaternion matrix equations with multiple unknowns

CQ Zhang, QW Wang, A Dmytryshyn, ZH He - Computational and Applied …, 2024‏ - Springer
In this paper, we consider the solvability conditions of some Sylvester-type quaternion matrix
equations. We establish some practical necessary and sufficient conditions for the existence …

Some new results on a system of Sylvester-type quaternion matrix equations

ZH He - Linear and Multilinear Algebra, 2021‏ - Taylor & Francis
In this paper, we establish a different approach for solving the system of three coupled two-
sided Sylvester-type quaternion matrix equations A i X i B i+ C i X i+ 1 D i= E i, i= 1, 3¯. We …

The general -Hermitian solution to mixed pairs of quaternion matrix Sylvester equations

ZH He, J Liu, TY Tam - The Electronic Journal of Linear Algebra, 2017‏ - journals.uwyo.edu
Abstract Let $\mathbb {H}^{m\times n} $ be the space of $ m\times n $ matrices over
$\mathbb {H} $, where $\mathbb {H} $ is the real quaternion algebra. Let $ A_ {\phi} $ be the …

[HTML][HTML] Two-sided coupled generalized Sylvester matrix equations solving using a simultaneous decomposition for fifteen matrices

ZH He, OM Agudelo, QW Wang, B De Moor - Linear Algebra and its …, 2016‏ - Elsevier
In this paper, we investigate and analyze in detail the structure and properties of a
simultaneous decomposition for fifteen matrices: A i∈ C pi× ti, B i∈ C si× qi, C i∈ C pi× t i+ …

[HTML][HTML] Uniqueness of solution of a generalized⋆-Sylvester matrix equation

F De Teran, B Iannazzo - Linear Algebra and its Applications, 2016‏ - Elsevier
We present necessary and sufficient conditions for the existence of a unique solution of the
generalized⋆-Sylvester matrix equation AX B+ CX⋆ D= E, where A, B, C, D, E are square …

[کتاب][B] Complex conjugate matrix equations for systems and control

AG Wu, Y Zhang - 2017‏ - Springer
Theory of matrix equations is an important branch of mathematics, and has broad
applications in many engineering fields, such as control theory, information theory, and …

[HTML][HTML] Solvability and uniqueness criteria for generalized Sylvester-type equations

F De Terán, B Iannazzo, F Poloni, L Robol - Linear algebra and its …, 2018‏ - Elsevier
We provide necessary and sufficient conditions for the generalized⋆-Sylvester matrix
equation, AX B+ CX⋆ D= E, to have exactly one solution for any right-hand side E. These …