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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| Дата: | 2021 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2021
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1461 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | 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. |
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