{"title":"Tridiagonal M-matrices whose group inverses are tridiagonal","authors":"A.M. Encinas , K. Kranthi Priya , K.C. Sivakumar","doi":"10.1016/j.laa.2024.11.026","DOIUrl":null,"url":null,"abstract":"<div><div>Recently, a characterization was obtained for a nonsingular <em>M</em>-matrix, to have a tridiagonal inverse. In a related work, the explicit sign pattern for this kind of matrices was also discovered. In this paper, we extend these results to singular <em>M</em>-matrices that are group invertible. Further, we obtain the precise sign pattern for such matrices. Our techniques and reasoning work for both singular and nonsingular matrices, thereby providing a unified framework to treat such classes of matrices.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"708 ","pages":"Pages 42-60"},"PeriodicalIF":1.1000,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Linear Algebra and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S002437952400452X","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/11/29 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Recently, a characterization was obtained for a nonsingular M-matrix, to have a tridiagonal inverse. In a related work, the explicit sign pattern for this kind of matrices was also discovered. In this paper, we extend these results to singular M-matrices that are group invertible. Further, we obtain the precise sign pattern for such matrices. Our techniques and reasoning work for both singular and nonsingular matrices, thereby providing a unified framework to treat such classes of matrices.
期刊介绍：
Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.
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