An algebraic-analytic approach to nonnegative bases
For a nonnegative \(n\times n\) matrix A let \(W_ A\) be the algebraic eigenspace corresponding to the Perron root of A, which is equal to the spectral radius \(\rho\) (A). Using the Laurent expansion of the resolvent operator \((\lambda I-A)^{-1}\) in a deleted neighborhood of \(\lambda =\rho (A)\), the authors give new proofs for the following two results due to \textit{U. G. Rothblum} [ibid. 12, 281-292 (1975; Zbl 0321.15010)]: (i) \(W_ A\) has a basis of nonnegative vectors, (ii) \(W_ A\) has a Jordan chain of maximal length consisting entirely of nonnegative vectors. A simple and elegant algorithm for determining a nonnegative basis of \(W_ A\) (which is not necessarily a Jordan chain) is also presented.
scientific article; zbMATH DE number 4163077
scientific article