About the spectra of a real nonnegative matrix and its signings
For a complex matrix \(M\), we denote by \(\operatorname{Sp}(M)\) the spectrum of \(M\) and by \(|M|\) its absolute value, that is the matrix obtained from \(M\) by replacing each entry of \(M\) by its absolute value. Let \(A\) be a nonnegative real matrix, we call a signing of \(A\) every real matr...
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| Date: | 2021 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2021
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1461 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543053467090944 |
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| author | Attas, K. Boussaïri, A. Zaidi, M. |
| author_facet | Attas, K. Boussaïri, A. Zaidi, M. |
| author_sort | Attas, K. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2021-11-09T03:53:16Z |
| description | For a complex matrix \(M\), we denote by \(\operatorname{Sp}(M)\) the spectrum of \(M\) and by \(|M|\) its absolute value, that is the matrix obtained from \(M\) by replacing each entry of \(M\) by its absolute value. Let \(A\) be a nonnegative real matrix, we call a signing of \(A\) every real matrix \(B\) such that \(|B| =A\). In this paper, we characterize the set of all signings of \(A\) such that \(\operatorname{Sp}(B)=\alpha \operatorname{Sp}(A)\) where \(\alpha\) is a complex unit number. Our motivation comes from some recent results about the relationship between the spectrum of a graph and the skew spectra of its orientations. |
| first_indexed | 2025-12-02T15:30:10Z |
| format | Article |
| id | admjournalluguniveduua-article-1461 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:30:10Z |
| publishDate | 2021 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-14612021-11-09T03:53:16Z About the spectra of a real nonnegative matrix and its signings Attas, K. Boussaïri, A. Zaidi, M. spectra, digraphs, nonnegative matrices, irreducible matrices 05C20, 05C50 For a complex matrix \(M\), we denote by \(\operatorname{Sp}(M)\) the spectrum of \(M\) and by \(|M|\) its absolute value, that is the matrix obtained from \(M\) by replacing each entry of \(M\) by its absolute value. Let \(A\) be a nonnegative real matrix, we call a signing of \(A\) every real matrix \(B\) such that \(|B| =A\). In this paper, we characterize the set of all signings of \(A\) such that \(\operatorname{Sp}(B)=\alpha \operatorname{Sp}(A)\) where \(\alpha\) is a complex unit number. Our motivation comes from some recent results about the relationship between the spectrum of a graph and the skew spectra of its orientations. Lugansk National Taras Shevchenko University 2021-11-09 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1461 10.12958/adm1461 Algebra and Discrete Mathematics; Vol 32, No 1 (2021) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1461/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1461/584 Copyright (c) 2021 Algebra and Discrete Mathematics |
| spellingShingle | spectra digraphs nonnegative matrices irreducible matrices 05C20 05C50 Attas, K. Boussaïri, A. Zaidi, M. About the spectra of a real nonnegative matrix and its signings |
| title | About the spectra of a real nonnegative matrix and its signings |
| title_full | About the spectra of a real nonnegative matrix and its signings |
| title_fullStr | About the spectra of a real nonnegative matrix and its signings |
| title_full_unstemmed | About the spectra of a real nonnegative matrix and its signings |
| title_short | About the spectra of a real nonnegative matrix and its signings |
| title_sort | about the spectra of a real nonnegative matrix and its signings |
| topic | spectra digraphs nonnegative matrices irreducible matrices 05C20 05C50 |
| topic_facet | spectra digraphs nonnegative matrices irreducible matrices 05C20 05C50 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1461 |
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