文献类型：期刊文献

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

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

年份：2021

卷号：393

外文期刊名：JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

收录：;EI(收录号：20211010029498);WOS:【SCI-EXPANDED(收录号:WOS:000640527200003)】；

基金：This research was supported by the grants from the National Natural Science Foundation of China (11801354).

语种：英文

外文关键词：Quaternion matrix decomposition; Quaternion matrix equation; General solution; Solvability; Imaging

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.