{"title":"Irreducible matrix representations of quaternions","authors":"Yu Chen","doi":"10.1016/j.laa.2024.11.010","DOIUrl":null,"url":null,"abstract":"<div><div>We determine all irreducible real and complex matrix representations of quaternions and classify them up to equivalence. More over, we show that there is a one-to-one correspondence between the equivalence classes of the irreducible matrix representations and those of the field homomorphisms from the real numbers to the complex numbers.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"706 ","pages":"Pages 55-69"},"PeriodicalIF":1.0000,"publicationDate":"2024-11-17","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/S0024379524004300","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We determine all irreducible real and complex matrix representations of quaternions and classify them up to equivalence. More over, we show that there is a one-to-one correspondence between the equivalence classes of the irreducible matrix representations and those of the field homomorphisms from the real numbers to the complex numbers.
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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