A characterization of trace zero symmetric nonnegative \(5\times 5\) matrices. (English) Zbl 1209.15037
The problem of determining necessary and sufficient conditions for a set of real numbers to be the eigenvalues of an \(n \times n\) symmetric non-negative matrix is called the symmetric non-negative inverse eigenvalue problem (SNIEP). The problem is completely solved only for \(n\leq 4\). For \(n=5\), R. Loewy and J. J. McDonald [Linear Algebra Appl. 393, 275–298 (2004; Zbl 1066.15007)] obtained a partial solution for nonnegative symmetric matrices with non-zero trace. In this paper, the author solves the SNIEP for the trace zero symmetric nonnegative \(5 \times 5\) matrices. The problem in the general case is still unsolved.
Reviewer: Krishnendu Gongopadhyay (Mohali)
MSC:
| 15B48 | Positive matrices and their generalizations; cones of matrices |
| 15A29 | Inverse problems in linear algebra |
| 15B57 | Hermitian, skew-Hermitian, and related matrices |
| 15A18 | Eigenvalues, singular values, and eigenvectors |
Keywords:
SNIEPCitations:
Zbl 1066.15007References:
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