A Perron-Frobenius Theorem for Positive Quasipolynomial Matrices Associated with Homogeneous Difference Equations

A Perron-Frobenius Theorem for Positive Quasipolynomial Matrices Associated with Homogeneous Difference Equations

Generalized Perron-Frobenius Theorem for Nonsquare Matrices

The celebrated Perron–Frobenius (PF) theorem is stated for irreducible nonnegative square matrices, and provides a simple characterization of their eigenvectors and eigenvalues. The importance of this theorem stems from the fact that eigenvalue problems on such matrices arise in many fields of science and engineering, including dynamical systems theory, economics, statistics and optimization. H...

The Perron-frobenius Theorem for Homogeneous, Monotone Functions

If A is a nonnegative matrix whose associated directed graph is strongly connected, the Perron-Frobenius theorem asserts that A has an eigenvector in the positive cone, (R). We associate a directed graph to any homogeneous, monotone function, f : (R) → (R), and show that if the graph is strongly connected then f has a (nonlinear) eigenvector in (R). Several results in the literature emerge as c...

Generalized Perron-Frobenius Theorem for Multiple Choice Matrices, and Applications

The celebrated Perron–Frobenius (PF) theorem is stated for irreducible nonnegative square matrices, and provides a simple characterization of their eigenvectors and eigenvalues. The importance of this theorem stems from the fact that eigenvalue problems on such matrices arise in many fields of science and engineering, including dynamical systems theory, economics, statistics and optimization. H...

Stochastic Nonlinear Perron-frobenius Theorem∗

We establish a stochastic nonlinear analogue of the PerronFrobenius theorem on eigenvalues and eigenvectors of positive matrices. The result is formulated in terms of an automorphism T of a probability space (Ω,F , P ) and a random mapping D(ω, ·) : R+ → R+. Under assumptions of monotonicity and homogeneity of D(ω, ·), we prove the existence of scalar and vector measurable functions α(ω) > 0 an...