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A characterization of trace zero nonnegative \(5\times 5\) matrices. (English) Zbl 0946.15008

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.

MSC:

15A29 Inverse problems in linear algebra
15A18 Eigenvalues, singular values, and eigenvectors
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