正交、对称和斜对称矩阵的和

Pub Date : 2022-10-07 DOI:10.13001/ela.2022.7129

Ralph John de la Cruz, Agnes T. Paras

{"title":"正交、对称和斜对称矩阵的和","authors":"Ralph John de la Cruz, Agnes T. Paras","doi":"10.13001/ela.2022.7129","DOIUrl":null,"url":null,"abstract":"An $n$-by-$n$ matrix $A$ is called symmetric, skew-symmetric, and orthogonal if $A^T=A$, $A^T=-A$, and $A^T=A^{-1}$, respectively. We give necessary and sufficient conditions on a complex matrix $A$ so that it is a sum of type ``\"orthogonal $+$ symmetric\" in terms of the Jordan form of $A-A^T$. We also give necessary and sufficient conditions on a complex matrix $A$ so that it is a sum of type \"orthogonal $+$ skew-symmetric\" in terms of the Jordan form of $A+A^T$.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Sums of orthogonal, symmetric, and skew-symmetric matrices\",\"authors\":\"Ralph John de la Cruz, Agnes T. Paras\",\"doi\":\"10.13001/ela.2022.7129\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An $n$-by-$n$ matrix $A$ is called symmetric, skew-symmetric, and orthogonal if $A^T=A$, $A^T=-A$, and $A^T=A^{-1}$, respectively. We give necessary and sufficient conditions on a complex matrix $A$ so that it is a sum of type ``\\\"orthogonal $+$ symmetric\\\" in terms of the Jordan form of $A-A^T$. We also give necessary and sufficient conditions on a complex matrix $A$ so that it is a sum of type \\\"orthogonal $+$ skew-symmetric\\\" in terms of the Jordan form of $A+A^T$.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2022-10-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.13001/ela.2022.7129\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.13001/ela.2022.7129","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

如果$A^T=A$、$A^T=-A$和$A^T=A^{-1}$，则一个$n$ × $n$矩阵$A$分别称为对称、偏对称和正交矩阵$A$。给出了复矩阵$ a $在$ a - a ^T$的约当形式下是“正交$+对称$”型和的充要条件。我们还给出了复矩阵$ a $在$ a + a ^T$的约当形式下是“正交$+$偏对称”型和的充要条件。

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

Sums of orthogonal, symmetric, and skew-symmetric matrices

An $n$-by-$n$ matrix $A$ is called symmetric, skew-symmetric, and orthogonal if $A^T=A$, $A^T=-A$, and $A^T=A^{-1}$, respectively. We give necessary and sufficient conditions on a complex matrix $A$ so that it is a sum of type ``"orthogonal $+$ symmetric" in terms of the Jordan form of $A-A^T$. We also give necessary and sufficient conditions on a complex matrix $A$ so that it is a sum of type "orthogonal $+$ skew-symmetric" in terms of the Jordan form of $A+A^T$.

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