{"title":"Study on the Similarity between Nonnegative Irreducible Matrices and Positive Matrices","authors":"Hao Zhang","doi":"10.56028/aetr.8.1.133.2023","DOIUrl":null,"url":null,"abstract":"The main objective of this study is to explore the problem of similarity between nonnegative irreducible matrices and positive matrices. By leveraging established lemmas and drawing insights from pertinent literature, this article provides a rigorous proof: When is greater than 8, for any nonnegative irreducible matrix , if it contains zero elements and possesses mutually distinct diagonal elements, then is similar to a positive matrix.","PeriodicalId":502380,"journal":{"name":"Advances in Engineering Technology Research","volume":"33 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Engineering Technology Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.56028/aetr.8.1.133.2023","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The main objective of this study is to explore the problem of similarity between nonnegative irreducible matrices and positive matrices. By leveraging established lemmas and drawing insights from pertinent literature, this article provides a rigorous proof: When is greater than 8, for any nonnegative irreducible matrix , if it contains zero elements and possesses mutually distinct diagonal elements, then is similar to a positive matrix.
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