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An inequality for nonnegative matrices and the inverse eigenvalue problem. (English) Zbl 0887.15015

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.

MSC:

15A42 Inequalities involving eigenvalues and eigenvectors
15A18 Eigenvalues, singular values, and eigenvectors
15A23 Factorization of matrices
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References:

[1] DOI: 10.1215/S0012-7094-52-01910-8 · Zbl 0046.01202
[2] DOI: 10.2307/2944339 · Zbl 0735.15005
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[4] DOI: 10.1080/03081088108817402 · Zbl 0455.15019
[5] DOI: 10.1080/03081087808817226 · Zbl 0376.15006
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[8] van der Waerden B. L., Modern Algebra 1 (1988)
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