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Constructions of potentially eventually positive sign patterns with reducible positive part. (English) Zbl 1252.15033

Summary: Potentially eventually positive (PEP) sign patterns were introduced by A. Berman et al. [Electron. J. Linear Algebra 19, 108–120 (2010; Zbl 1190.15031)], where it was noted that a matrix is PEP if its positive part is primitive, and an example was given of a \(3 \times 3\) PEP sign pattern with reducible positive part. We extend these results by constructing \(n \times n\) PEP sign patterns with reducible positive part, for every \(n \geq 3\).

MSC:

15B35 Sign pattern matrices
15B48 Positive matrices and their generalizations; cones of matrices
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
15A18 Eigenvalues, singular values, and eigenvectors

Citations:

Zbl 1190.15031
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