Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



A simple approach to the Perron-Frobenius theory for positive operators on general partially-ordered finite-dimensional linear spaces

Authors: Werner C. Rheinboldt and James S. Vandergraft
Journal: Math. Comp. 27 (1973), 139-145
MSC: Primary 15A48
MathSciNet review: 0325650
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: This paper presents simple proofs of the principal results of the Perron-Frobenius theory for linear mappings on finite-dimensional spaces which are nonnegative relative to a general partial ordering on the space. The principal tool for these proofs is an application of the theory of norms in finite dimensions to the study of order inequalities of the form $ Ax \leqq \alpha x,x \geqq 0$ where $ A \geqq 0$. This approach also permits the derivation of various inclusion and comparison theorems.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 15A48

Retrieve articles in all journals with MSC: 15A48

Additional Information

Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society