On the distinguished eigenvalues of a cone-preserving map
type: Item
instance of: scholarly article
title: On the distinguished eigenvalues of a cone-preserving map
zbMATH Open document ID: 0699.15007
DOI: 10.1016/0024-3795(90)90372-J
published in: Linear Algebra and its Applications
publication date: 1990-01-01T00:00:00Z
review text: Let A be a linear map which takes some proper cone K into itself. It is well known that the spectral radius of A is an eigenvalue and that there is a corresponding eigenvector in K. An eigenvalue of A is termed distinguished if there is a corresponding eigenvector in K. The author extends some results to the study of the Collatz-Wielandt sets which contain the distinguished eigenvalues. He then gives a cone theoretic proof for the existence of a nonnegative basis for the algebraic eigenspace of an (entrywise) nonnegative matrix. He then relates this to spectral properties of a map which preserves a polyhedral cone.
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 4146167
zbMATH Keywords: cone preserving maps
zbMATH Keywords: spectral radius
zbMATH Keywords: eigenvalue
zbMATH Keywords: eigenvector
zbMATH Keywords: Collatz- Wielandt sets
zbMATH Keywords: distinguished eigenvalues
zbMATH Keywords: nonnegative basis
zbMATH Keywords: algebraic eigenspace
author: Bit-Shun Tam
reviewed by: George Phillip Barker
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4146167