{"title":"二元矩阵方程 AXB=B=BXA 系统在两个部分阶中的解","authors":"Xiaoji Liu , Yuyan Chen , Hongxing Wang","doi":"10.1016/j.kjs.2024.100325","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we consider the solutions of the system of dual matrix equation <span><math><mrow><mi>A</mi><mi>X</mi><mi>B</mi><mo>=</mo><mi>B</mi><mo>=</mo><mi>B</mi><mi>X</mi><mi>A</mi></mrow></math></span> in P-star partial order and D-star partial order, respectively. The solvability condition are obtained by applying the singular value decomposition (SVD) and the expression of general solutions to the dual matrix equations are provided. The special case in which <span><math><mrow><mi>A</mi><mo>=</mo><mi>B</mi></mrow></math></span> is discussed and the properties of <span><math><mrow><mrow><mo>{</mo><mn>1</mn><mo>}</mo></mrow><mo>−</mo></mrow></math></span>dual generalized inverse are used to verify the accuracy of the explicit solution of dual matrix equation <span><math><mrow><mi>B</mi><mi>X</mi><mi>B</mi><mo>=</mo><mi>B</mi></mrow></math></span>. Finally, the explicit formula for the unique minimum-norm solution is given.</div></div>","PeriodicalId":17848,"journal":{"name":"Kuwait Journal of Science","volume":"52 1","pages":"Article 100325"},"PeriodicalIF":1.2000,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Solutions of the system of dual matrix equation AXB=B=BXA in two partial orders\",\"authors\":\"Xiaoji Liu , Yuyan Chen , Hongxing Wang\",\"doi\":\"10.1016/j.kjs.2024.100325\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, we consider the solutions of the system of dual matrix equation <span><math><mrow><mi>A</mi><mi>X</mi><mi>B</mi><mo>=</mo><mi>B</mi><mo>=</mo><mi>B</mi><mi>X</mi><mi>A</mi></mrow></math></span> in P-star partial order and D-star partial order, respectively. The solvability condition are obtained by applying the singular value decomposition (SVD) and the expression of general solutions to the dual matrix equations are provided. The special case in which <span><math><mrow><mi>A</mi><mo>=</mo><mi>B</mi></mrow></math></span> is discussed and the properties of <span><math><mrow><mrow><mo>{</mo><mn>1</mn><mo>}</mo></mrow><mo>−</mo></mrow></math></span>dual generalized inverse are used to verify the accuracy of the explicit solution of dual matrix equation <span><math><mrow><mi>B</mi><mi>X</mi><mi>B</mi><mo>=</mo><mi>B</mi></mrow></math></span>. Finally, the explicit formula for the unique minimum-norm solution is given.</div></div>\",\"PeriodicalId\":17848,\"journal\":{\"name\":\"Kuwait Journal of Science\",\"volume\":\"52 1\",\"pages\":\"Article 100325\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-09-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Kuwait Journal of Science\",\"FirstCategoryId\":\"103\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2307410824001500\",\"RegionNum\":4,\"RegionCategory\":\"综合性期刊\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kuwait Journal of Science","FirstCategoryId":"103","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2307410824001500","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
引用次数: 0
摘要
本文分别考虑双矩阵方程 AXB=B=BXA 系统在 P 星部分阶和 D 星部分阶的解。通过应用奇异值分解（SVD）得到了可解条件，并提供了对偶矩阵方程一般解的表达式。讨论了 A=B 的特殊情况，并利用 {1} 对偶广义逆的性质验证了对偶矩阵方程 BXB=B 的显解的准确性。最后，给出了唯一最小规范解的显式。
Solutions of the system of dual matrix equation AXB=B=BXA in two partial orders
In this paper, we consider the solutions of the system of dual matrix equation in P-star partial order and D-star partial order, respectively. The solvability condition are obtained by applying the singular value decomposition (SVD) and the expression of general solutions to the dual matrix equations are provided. The special case in which is discussed and the properties of dual generalized inverse are used to verify the accuracy of the explicit solution of dual matrix equation . Finally, the explicit formula for the unique minimum-norm solution is given.
期刊介绍：
Kuwait Journal of Science (KJS) is indexed and abstracted by major publishing houses such as Chemical Abstract, Science Citation Index, Current contents, Mathematics Abstract, Micribiological Abstracts etc. KJS publishes peer-review articles in various fields of Science including Mathematics, Computer Science, Physics, Statistics, Biology, Chemistry and Earth & Environmental Sciences. In addition, it also aims to bring the results of scientific research carried out under a variety of intellectual traditions and organizations to the attention of specialized scholarly readership. As such, the publisher expects the submission of original manuscripts which contain analysis and solutions about important theoretical, empirical and normative issues.
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