The peripheral spectrum of a nonnegative matrix
A link between the Tam-Schneider condition [cf. \textit{B.-S. Tam} and \textit{H. Schneider}, Trans. Am. Math. Soc. 343, 479-524 (1994; Zbl 0826.15015)] on the peripheral spectrum of a nonnegative matrix \(A\), to the peripheral spectrum of the submatrix of \(A\) associated with the highest level set (levels are taken with respect to the spectral radius) is established. By extending this condition to all level sets, new necessary conditions on the Jordan form of the peripheral spectrum are provided and using a construction method for eventually nonnegative matrices it is shown that these conditions are also sufficient.
scientific article; zbMATH DE number 1903569
scientific article