Nonlinear Perron-Frobenius theory

Nonlinear Perron-Frobenius theory / Bas Lemmens, Roger Nussbaum.

In the past several decades the classical Perron-Frobenius theory for nonnegative matrices has been extended to obtain remarkably precise and beautiful results for classes of nonlinear maps. This nonlinear Perron-Frobenius theory has found significant uses in computer science, mathematical biology,...

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Bibliographic Details
Other Authors: Lemmens, Bas, Nussbaum, Roger D., 1944-
Format: eBook
Language:English
Published: Cambridge : Cambridge University Press, 2012.
Series:Cambridge tracts in mathematics ; 189.
Subjects:
Non-negative matrices.
Eigenvalues.
Eigenvectors.
Algebras, Linear.
MATHEMATICS > Differential Equations.
MATHEMATICS > Algebra > Linear.
Álgebra lineal
Matrices no negativas
Algebras, Linear
Eigenvalues
Eigenvectors
Non-negative matrices
Online Access:Click for online access
Table of Contents:
  • Cover; CAMBRIDGE TRACTS IN MATHEMATICS; GENERAL EDITORS; Title; Copyright; Contents; Preface; 1 What is nonlinear Perron-Frobenius theory?; 1.1 Classical Perron-Frobenius theory; 1.2 Cones and partial orderings; 1.3 Order-preserving maps; 1.4 Subhomogeneous maps; 1.5 Topical maps; 1.6 Integral-preserving maps; 2 Non-expansiveness and nonlinear Perron-Frobenius theory; 2.1 Hilbert's and Thompson's metrics; 2.2 Polyhedral cones; 2.3 Lorentz cones; 2.4 The cone of positive-semidefinite symmetric matrices; 2.5 Completeness; 2.6 Convexity and geodesics; 2.7 Topical maps and the sup-norm.

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