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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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