{"title":"On invertibility and group inverse of combinations of two orthogonal projectors about a complex square matrix","authors":"Yinlan Chen","doi":"10.1109/ICACI.2017.7974479","DOIUrl":null,"url":null,"abstract":"For any complex square matrix A, this paper characterizes the invertibility and group inverse of the combinations P = a<inf>1</inf> P<inf>R(A)</inf> + a<inf>2</inf> P<inf>R(A∗)</inf> +a<inf>3</inf> P<inf>R(A)</inf> P<inf>R(A∗)</inf> +a<inf>4</inf> P<inf>R(A∗)</inf> P<inf>R(A)</inf> by M-C-S decomposition of A. Necessary and sufficient conditions of the invertibility and its inverse are presented completely. Also, we characterize the group inverse and give an expression for P<sup>#</sup> when P is group invertible.","PeriodicalId":260701,"journal":{"name":"2017 Ninth International Conference on Advanced Computational Intelligence (ICACI)","volume":"79 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2017 Ninth International Conference on Advanced Computational Intelligence (ICACI)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICACI.2017.7974479","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
For any complex square matrix A, this paper characterizes the invertibility and group inverse of the combinations P = a1 PR(A) + a2 PR(A∗) +a3 PR(A) PR(A∗) +a4 PR(A∗) PR(A) by M-C-S decomposition of A. Necessary and sufficient conditions of the invertibility and its inverse are presented completely. Also, we characterize the group inverse and give an expression for P# when P is group invertible.
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