{"title":"非负不可还原矩阵与正矩阵相似性研究","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":"{\"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}","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}
Study on the Similarity between Nonnegative Irreducible Matrices and Positive Matrices
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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