ON GENERAL MATRICES HAVING THE PERRON-FROBENIUS PROPERTY ∗
By Abed Elhashash, Daniel B. Szyld. 2008
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A matrix is said to have the Perron-Frobenius propertyif its spectral radius is an eigenvalue with a corresponding nonnegative eigenvector. Matrices having this and similar properties are studied in this paper as generalizations of nonnegative matrices. Sets consisting of such gener- alized nonnegative matrices are studied and certain topological aspects such as connectedness and closure are proved. Similaritytransformations leaving such sets invariant are completelydescribed, and it is shown that a nonnilpotent matrix eventuallycapturing the Perron-Frobenius propertyis in fact a matrix that alreadyhas it.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Electrical and Electronic Engineering
View Paper: https://www.semanticscholar.org/paper/310c752e5157f4b7eae4891910c91adb32459464
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Citations in the corpus
- Eventually and asymptotically positive semigroups on Banach lattices (2015, background): “ of inverse eigenvalues problems (see e.g. [11, 27, 57] or [50, pp. 48–54]) and by an attempt to generalise the classical Perron–Frobenius type spectral results to a wider class of matrices (see e.g. [21, 37]). An analysis of continuous-time eventually positive matrix semigroups can for example be f”