The equivalence canonical form of five quaternion matrices with applications to imaging and Sylvester-type equations

被引：23

作者：

Yu, Shao-Wen ^{[1
]}

He, Zhuo-Heng ^{[2
]}

Qi, Tian-Cheng ^{[2
]}

Wang, Xiang-Xiang ^{[2
]}

机构：

[1] East China Univ Sci & Technol, Dept Math, Shanghai, Peoples R China

[2] Shanghai Univ, Dept Math, Shanghai, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2021年 / 393卷

基金：

中国国家自然科学基金;

关键词：

Quaternion matrix decomposition; Quaternion matrix equation; General solution; Solvability; Imaging; STRUCTURE-PRESERVING METHOD; SINGULAR-VALUE; AX; DECOMPOSITION; SYSTEMS; ROBUST;

D O I：

10.1016/j.cam.2021.113494

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The equivalence canonical form of five quaternion matrices is investigated. Applications that are discussed include Sylvester-type quaternion matrix equations and color image encryption. A system of one-sided Sylvester-type quaternion matrix equations with six unknowns and five equations is considered by using this equivalence canonical form. Two different types of necessary and sufficient conditions for a solution to this system in terms of ranks and block matrices are presented. An expression of the general solution to the system is provided when it is solvable. Five color images can be encrypted simultaneously by using this equivalence canonical form. Some algorithms and examples are given to illustrate the main result. (c) 2021 Elsevier B.V. All rights reserved.

引用

页数：20

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