A simplification of the C-realizability criterion for the Nonnegative Inverse Eigenvalue Problem for integers
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917568027033600 |
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| author | Borobia, Alberto Canogar, Roberto |
| author_facet | Borobia, Alberto Canogar, Roberto |
| contents | A multiset $Λ=\{λ_1,\ldots,λ_n\}$ of complex numbers is said to be realizable whenever there exists a nonnegative matrix of order $n$ with spectrum $Λ$. One of the broadest criterion that guarantees realizability is the $C-$realizability. It says that $Λ$, with real numbers, is $C-$realizable if it can be obtained starting from $n$ basic multisets $\{0\},\ldots,\{0\}$ by successively applying any finite number of times any of the following rules: (a) join two of the multisets; (b) increase by $ε>0$ the Perron root of one of the multisets; (c) increase by $ε>0$ the Perron root of one of the multisets and simultaneously increase or decrease by $ε$ any other value of the same multiset. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_07857 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A simplification of the C-realizability criterion for the Nonnegative Inverse Eigenvalue Problem for integers Borobia, Alberto Canogar, Roberto Spectral Theory 15A18, 15A29 A multiset $Λ=\{λ_1,\ldots,λ_n\}$ of complex numbers is said to be realizable whenever there exists a nonnegative matrix of order $n$ with spectrum $Λ$. One of the broadest criterion that guarantees realizability is the $C-$realizability. It says that $Λ$, with real numbers, is $C-$realizable if it can be obtained starting from $n$ basic multisets $\{0\},\ldots,\{0\}$ by successively applying any finite number of times any of the following rules: (a) join two of the multisets; (b) increase by $ε>0$ the Perron root of one of the multisets; (c) increase by $ε>0$ the Perron root of one of the multisets and simultaneously increase or decrease by $ε$ any other value of the same multiset. |
| title | A simplification of the C-realizability criterion for the Nonnegative Inverse Eigenvalue Problem for integers |
| topic | Spectral Theory 15A18, 15A29 |
| url | https://arxiv.org/abs/2401.07857 |