关于实四元数的基本自旋矩阵

Q3 Mathematics

WSEAS Transactions on Mathematics Pub Date : 2023-11-15 DOI:10.37394/23206.2023.22.93

Tülay Erişir, Emrah Yildirim

{"title":"关于实四元数的基本自旋矩阵","authors":"Tülay Erişir, Emrah Yildirim","doi":"10.37394/23206.2023.22.93","DOIUrl":null,"url":null,"abstract":"In this study, the real quaternions and spinors are studied. The motivation of this study is to express the Hamilton matrices of real quaternions more shortly and elegantly, namely spinors. Therefore, firstly, two transformations between real quaternions and spinors are defined. These transformations are defined for two different spinor matrices corresponding to the left and right Hamilton matrices since the quaternion product is not commutative. Thus, the fundamental spinor matrix corresponding to the fundamental matrix of real quaternions is obtained and some properties are given for these spinor matrices. Finally, the eigenvalues and eigenvectors of the fundamental spinor matrix are obtained.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"69 2","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Fundamental Spinor Matrices of Real Quaternions\",\"authors\":\"Tülay Erişir, Emrah Yildirim\",\"doi\":\"10.37394/23206.2023.22.93\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this study, the real quaternions and spinors are studied. The motivation of this study is to express the Hamilton matrices of real quaternions more shortly and elegantly, namely spinors. Therefore, firstly, two transformations between real quaternions and spinors are defined. These transformations are defined for two different spinor matrices corresponding to the left and right Hamilton matrices since the quaternion product is not commutative. Thus, the fundamental spinor matrix corresponding to the fundamental matrix of real quaternions is obtained and some properties are given for these spinor matrices. Finally, the eigenvalues and eigenvectors of the fundamental spinor matrix are obtained.\",\"PeriodicalId\":55878,\"journal\":{\"name\":\"WSEAS Transactions on Mathematics\",\"volume\":\"69 2\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-11-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"WSEAS Transactions on Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37394/23206.2023.22.93\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"WSEAS Transactions on Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37394/23206.2023.22.93","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 0

摘要

本研究对实四元数和旋量进行了研究。本研究的动机是更简洁、优雅地表达实四元数的汉密尔顿矩阵，即旋量。因此，首先定义了实四元数和旋量之间的两种变换。由于四元积不是交换的，因此这些变换是针对与左右汉密尔顿矩阵相对应的两个不同的旋量矩阵定义的。这样，就得到了与实四元数基本矩阵相对应的基本旋量矩阵，并给出了这些旋量矩阵的一些性质。最后，还得到了基本旋量矩阵的特征值和特征向量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On the Fundamental Spinor Matrices of Real Quaternions

In this study, the real quaternions and spinors are studied. The motivation of this study is to express the Hamilton matrices of real quaternions more shortly and elegantly, namely spinors. Therefore, firstly, two transformations between real quaternions and spinors are defined. These transformations are defined for two different spinor matrices corresponding to the left and right Hamilton matrices since the quaternion product is not commutative. Thus, the fundamental spinor matrix corresponding to the fundamental matrix of real quaternions is obtained and some properties are given for these spinor matrices. Finally, the eigenvalues and eigenvectors of the fundamental spinor matrix are obtained.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

WSEAS Transactions on Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： WSEAS Transactions on Mathematics publishes original research papers relating to applied and theoretical mathematics. We aim to bring important work to a wide international audience and therefore only publish papers of exceptional scientific value that advance our understanding of these particular areas. The research presented must transcend the limits of case studies, while both experimental and theoretical studies are accepted. It is a multi-disciplinary journal and therefore its content mirrors the diverse interests and approaches of scholars involved with linear algebra, numerical analysis, differential equations, statistics and related areas. We also welcome scholarly contributions from officials with government agencies, international agencies, and non-governmental organizations.