{"title":"Weak star-Drazin and Drazin-star matrices","authors":"Dijana Mosić , Daochang Zhang","doi":"10.1016/j.disc.2024.114386","DOIUrl":null,"url":null,"abstract":"<div><div>Some systems of matrix equations weaker than existing are considered using a minimal rank weak Drazin inverse and a minimal rank right weak Drazin inverse. In order to solve new systems, we define weak star-Drazin and Drazin-star matrices which are new kinds of square matrices and generalizations of star-Drazin and Drazin-star matrices. Many characterizations and expressions of weak star-Drazin and Drazin-star matrices are proposed. As consequences, we recover known results and present new results about star-Drazin and Drazin-star matrices. Interesting special cases of weak star-Drazin and Drazin-star matrices are studied for the first time in the literature. We apply weak star-Drazin and Drazin-star matrices to solve some linear equations and present their general solution forms.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 4","pages":"Article 114386"},"PeriodicalIF":0.7000,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X2400517X","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/1/7 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Some systems of matrix equations weaker than existing are considered using a minimal rank weak Drazin inverse and a minimal rank right weak Drazin inverse. In order to solve new systems, we define weak star-Drazin and Drazin-star matrices which are new kinds of square matrices and generalizations of star-Drazin and Drazin-star matrices. Many characterizations and expressions of weak star-Drazin and Drazin-star matrices are proposed. As consequences, we recover known results and present new results about star-Drazin and Drazin-star matrices. Interesting special cases of weak star-Drazin and Drazin-star matrices are studied for the first time in the literature. We apply weak star-Drazin and Drazin-star matrices to solve some linear equations and present their general solution forms.
期刊介绍：
Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory.
Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.
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