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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Lugansk National Taras Shevchenko University
2021
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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 |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2021-11-09T03:53:16Z |
| collection |
OJS |
| language |
English |
| topic |
spectra digraphs nonnegative matrices irreducible matrices 05C20 05C50 |
| 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 |
| topic_facet |
spectra digraphs nonnegative matrices irreducible matrices 05C20 05C50 |
| format |
Article |
| author |
Attas, K. Boussaïri, A. Zaidi, M. |
| author_facet |
Attas, K. Boussaïri, A. Zaidi, M. |
| author_sort |
Attas, K. |
| title |
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_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_sort |
about the spectra of a real nonnegative matrix and its signings |
| 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2021 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1461 |
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AT attask aboutthespectraofarealnonnegativematrixanditssignings AT boussairia aboutthespectraofarealnonnegativematrixanditssignings AT zaidim aboutthespectraofarealnonnegativematrixanditssignings |
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2025-12-02T15:30:10Z |
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2025-12-02T15:30:10Z |
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1850412215661756416 |