A note for the SNIEP in size 5. (English) Zbl 1522.15018
The symmetric nonnegative inverse eigenvalue problem (SNIEP) is the problem of characterizing all possible real spectra of entrywise symmetric nonnegative matrices. A complete solution of this problem is known only for spectra of size \(n \le 4\). By elementary calculation, the authors establish the current state of the knowledge about the SNIEP of size \(5\) with just one repeated eigenvalue.
Reviewer: Tin Yau Tam (Reno)
MSC:
| 15A29 | Inverse problems in linear algebra |
| 15A18 | Eigenvalues, singular values, and eigenvectors |
| 15A42 | Inequalities involving eigenvalues and eigenvectors |
References:
| [1] | Johnson, C. R.; Marijuán, C.; Pisonero, M., Ruling out certain 5-spectra for the symmetric nonnegative inverse eigenvalue problem, Linear Algebra Appl., 512, 129-135 (2017) · Zbl 1353.15008 |
| [2] | Johnson, C. R.; Marijuán, C.; Pisonero, M., Ruling out certain 5-spectra with one repeated eigenvalue for the symmetric NIEP, Linear Algebra Appl., 612, 75-98 (2021) · Zbl 1458.15018 |
| [3] | Loewy, R.; Spector, O., A necessary condition for the spectrum of nonnegative symmetric \(5 \times 5\) matrices, Linear Algebra Appl., 528, 206-272 (2017) · Zbl 1398.15039 |
| [4] | Loewy, R., Some additional notes on the spectra of non-negative symmetric \(5 \times 5\) matrices, Electron. J. Linear Algebra, 37, 1-13 (2021) · Zbl 1465.15022 |
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