Laffey, Thomas J.; Meehan, Eleanor A characterization of trace zero nonnegative \(5\times 5\) matrices. (English) Zbl 0946.15008 Linear Algebra Appl. 302-303, 295-302 (1999). The determination of necessary and sufficient conditions for the existence of an entrywise nonnegative \(n \times n\) matrix \(A\) with spectrum \(\sigma\) is presented for the case \( n=5 \) with the trace equal to zero i. e. \(\lambda_1 +...+ \lambda_5 = 0\), where \(\lambda_i\) are complex numbers. This determination using the notion of \(n\)-cycle products is a part of the nonnegative inverse eigenvalue problem. Reviewer: Vaclav Burjan (Praha) Cited in 42 Documents MSC: 15A29 Inverse problems in linear algebra 15A18 Eigenvalues, singular values, and eigenvectors Keywords:nonnegative inverse eigenvalue problem; Petersen graph; cycles PDFBibTeX XMLCite \textit{T. J. Laffey} and \textit{E. Meehan}, Linear Algebra Appl. 302--303, 295--302 (1999; Zbl 0946.15008) Full Text: DOI References: [1] A. Berman, R. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, 1979; A. Berman, R. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, 1979 · Zbl 0484.15016 [2] Laffey, T. J.; Meehan, E., A refinement of an inequality of Johnson, Loewy and London on nonnegative matrices and some applications, ELA, 3, 119-128 (1998) · Zbl 0907.15013 [3] Loewy, R.; London, D., A note on the inverse eigenvalue problems for nonnegative matrices, Linear and Multilinear Algebra, 6, 83-90 (1978) · Zbl 0376.15006 [4] H. Mine, Nonnegative Matrices, Wiley, New York, 1988; H. Mine, Nonnegative Matrices, Wiley, New York, 1988 [5] Reams, R., Topics in Matrix Theory, Thesis presented for the degree of Ph.D. (1994), National University of Ireland: National University of Ireland Dublin [6] Reams, R., An inequality for nonnegative matrices and the inverse eigenvalue problem, Linear and Multilinear Algebra, 41, 367-375 (1996) · Zbl 0887.15015 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.