Realizable lists via the spectra of structured matrices
A square matrix of order $n$ with $n\geq 2$ is called a \textit{permutative matrix} or permutative when all its rows (up to the first one) are permutations of precisely its first row. In this paper, the spectra of a class of permutative matrices are studied. In particular, spectral results for matri...
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| Other Authors: | , |
| Format: | article |
| Language: | eng |
| Published: |
2017
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10773/18240 |
| Country: | Portugal |
| Oai: | oai:ria.ua.pt:10773/18240 |
| Summary: | A square matrix of order $n$ with $n\geq 2$ is called a \textit{permutative matrix} or permutative when all its rows (up to the first one) are permutations of precisely its first row. In this paper, the spectra of a class of permutative matrices are studied. In particular, spectral results for matrices partitioned into $2$-by-$2$ symmetric blocks are presented and, using these results sufficient conditions on a given list to be the list of eigenvalues of a nonnegative permutative matrix are obtained and the corresponding permutative matrices are constructed. Guo perturbations on given lists are exhibited. |
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