{"title":"Drazin theta and theta Drazin matrices","authors":"Divya P. Shenoy","doi":"10.3934/naco.2022023","DOIUrl":null,"url":null,"abstract":"<p style='text-indent:20px;'>In this paper, two new classes of matrices - Drazin - theta matrix and theta - Drazin matrix are introduced for a square matrix of index <inline-formula><tex-math id=\"M3\">\\begin{document}$ m $\\end{document}</tex-math></inline-formula>. Whenever the index is equal to one, we get special case of matrices called Group - theta matrix and theta - Group matrix respectively. Several characterizations of these matrices, the integral representations, representation in limit form and the representation in terms of rank factorization are obtained. Also, the relationship of Drazin -theta and theta - Drazin matrices with other well known generalized inverses are investigated. By applying the concept of Drazin - theta matrix, general solutions of certain types of matrix equations are characterized here.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/naco.2022023","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 2
Abstract
In this paper, two new classes of matrices - Drazin - theta matrix and theta - Drazin matrix are introduced for a square matrix of index \begin{document}$ m $\end{document}. Whenever the index is equal to one, we get special case of matrices called Group - theta matrix and theta - Group matrix respectively. Several characterizations of these matrices, the integral representations, representation in limit form and the representation in terms of rank factorization are obtained. Also, the relationship of Drazin -theta and theta - Drazin matrices with other well known generalized inverses are investigated. By applying the concept of Drazin - theta matrix, general solutions of certain types of matrix equations are characterized here.
In this paper, two new classes of matrices - Drazin - theta matrix and theta - Drazin matrix are introduced for a square matrix of index \begin{document}$ m $\end{document}. Whenever the index is equal to one, we get special case of matrices called Group - theta matrix and theta - Group matrix respectively. Several characterizations of these matrices, the integral representations, representation in limit form and the representation in terms of rank factorization are obtained. Also, the relationship of Drazin -theta and theta - Drazin matrices with other well known generalized inverses are investigated. By applying the concept of Drazin - theta matrix, general solutions of certain types of matrix equations are characterized here.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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