{"title":"A generalization of Fiedler's lemma and its applications","authors":"Yangyang Wu, Xiaoling Ma","doi":"10.1016/j.laa.2024.07.008","DOIUrl":null,"url":null,"abstract":"<div><p>In this article, taking a Fiedler's result on the spectrum of a matrix formed from two symmetric matrices as a motivation, we deduce a more general result on the eigenvalues of a matrix, which form from <em>n</em> symmetric matrices. As an important application, we obtain the adjacency spectra, Laplacian spectra and signless Laplacian spectra of a graph with a particular almost equitable partition.</p></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"699 ","pages":"Pages 604-620"},"PeriodicalIF":1.0000,"publicationDate":"2024-07-14","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/S0024379524002982","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
In this article, taking a Fiedler's result on the spectrum of a matrix formed from two symmetric matrices as a motivation, we deduce a more general result on the eigenvalues of a matrix, which form from n symmetric matrices. As an important application, we obtain the adjacency spectra, Laplacian spectra and signless Laplacian spectra of a graph with a particular almost equitable partition.
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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