Reams, Robert An inequality for nonnegative matrices and the inverse eigenvalue problem. (English) Zbl 0887.15015 Linear Multilinear Algebra 41, No. 4, 367-375 (1996). Two inequalities relating the spectrum of a nonnegative matrix to its maximal diagonal element are given. A solution of the nonnegative eigenvalue problem for \(n=4\) and trace zero is given, i.e., it is shown that in this case well-known necessary conditions on the spectrum are also sufficient to form the spectrum of a nonnegative matrix. Sufficient conditions for \(n=5\), trace zero are given. Also some further restricted cases are discussed. Reviewer: L.Elsner (Bielefeld) Cited in 36 Documents MSC: 15A42 Inequalities involving eigenvalues and eigenvectors 15A18 Eigenvalues, singular values, and eigenvectors 15A23 Factorization of matrices Keywords:inequality; inverse eigenvalue problem; companion matrix; nonnegative matrix; nonnegative eigenvalue problem; spectrum; trace PDFBibTeX XMLCite \textit{R. Reams}, Linear Multilinear Algebra 41, No. 4, 367--375 (1996; Zbl 0887.15015) Full Text: DOI References: [1] DOI: 10.1215/S0012-7094-52-01910-8 · Zbl 0046.01202 [2] DOI: 10.2307/2944339 · Zbl 0735.15005 [3] Berman A., Nonnegative Matrices in the Mathematical Sciences (1979) · Zbl 0484.15016 [4] DOI: 10.1080/03081088108817402 · Zbl 0455.15019 [5] DOI: 10.1080/03081087808817226 · Zbl 0376.15006 [6] Lancaster P., The Theory of Matrices, with Applications (1985) · Zbl 0558.15001 [7] Minc H., Nonnegative Matrices (1988) [8] van der Waerden B. L., Modern Algebra 1 (1988) 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.