具有η-Hermicity的四元数矩阵方程组的Cramer规则

4open Pub Date : 2019-01-01 DOI:10.1051/FOPEN/2019021

Ivan Kyrchei

{"title":"具有η-Hermicity的四元数矩阵方程组的Cramer规则","authors":"Ivan Kyrchei","doi":"10.1051/FOPEN/2019021","DOIUrl":null,"url":null,"abstract":"The system of two-sided quaternion matrix equations with η-Hermicity, A1XA1η* = C1, A2XA2η* = C2 is considered in the paper. Using noncommutative row-column determinants previously introduced by the author, determinantal representations (analogs of Cramer’s rule) of a general solution to the system are obtained. As special cases, Cramer’s rules for an η-Hermitian solution when C1 = Cη*1 and C2 = Cη*2 and for an η-skew-Hermitian solution when C1 = −Cη*1 and C2 = −Cη*2 are also explored.","PeriodicalId":6841,"journal":{"name":"4open","volume":"16 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Cramer’s rules for the system of quaternion matrix equations with η-Hermicity\",\"authors\":\"Ivan Kyrchei\",\"doi\":\"10.1051/FOPEN/2019021\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The system of two-sided quaternion matrix equations with η-Hermicity, A1XA1η* = C1, A2XA2η* = C2 is considered in the paper. Using noncommutative row-column determinants previously introduced by the author, determinantal representations (analogs of Cramer’s rule) of a general solution to the system are obtained. As special cases, Cramer’s rules for an η-Hermitian solution when C1 = Cη*1 and C2 = Cη*2 and for an η-skew-Hermitian solution when C1 = −Cη*1 and C2 = −Cη*2 are also explored.\",\"PeriodicalId\":6841,\"journal\":{\"name\":\"4open\",\"volume\":\"16 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"4open\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1051/FOPEN/2019021\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"4open","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1051/FOPEN/2019021","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 5

摘要

本文研究了具有η-Hermicity, A1XA1η* = C1, A2XA2η* = C2的双边四元数矩阵方程组。利用作者先前介绍的非交换行列行列式，得到了系统通解的行列式表示(类似于Cramer规则)。作为特殊情况，我们还探讨了当C1 = Cη*1和C2 = Cη*2时的η-厄米解和当C1 = - Cη*1和C2 = - Cη*2时的η-斜厄米解的Cramer规则。

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

Cramer’s rules for the system of quaternion matrix equations with η-Hermicity

The system of two-sided quaternion matrix equations with η-Hermicity, A1XA1η* = C1, A2XA2η* = C2 is considered in the paper. Using noncommutative row-column determinants previously introduced by the author, determinantal representations (analogs of Cramer’s rule) of a general solution to the system are obtained. As special cases, Cramer’s rules for an η-Hermitian solution when C1 = Cη*1 and C2 = Cη*2 and for an η-skew-Hermitian solution when C1 = −Cη*1 and C2 = −Cη*2 are also explored.

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

4open

自引率

0.00%

发文量