We prove several new versions of the Hadamard–Perron Theorem, which relates infinitesimal dynamics to local dynamics for a sequence of local diffeomorphisms, and in particular establishes the existence of local stable and unstable manifolds. Our results imply the classical Hadamard–Perron Theorem in both its uniform and non-uniform versions, but also apply much more generally. We introduce a no...

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...

MIPAS Level 1B algorithms overview: operational processing and characterization A. Kleinert, G. Aubertin, G. Perron, M. Birk, G. Wagner, F. Hase, H. Nett, and R. Poulin ABB Bomem Inc., 585 Blvd. Charest East, Québec, G1K 9H4, Canada Forschungszentrum Karlsruhe GmbH, Institut für Meteorologie und Klimaforschung, P.O. Box 3640, 76021 Karlsruhe, Germany Remote Sensing Technology Institute, German ...

This paper provides a simple proof for the Perron-Frobenius theorem concerned with positive matrices using a homotopy technique. By analyzing the behaviour of the eigenvalues of a family of positive matrices, we observe that the conclusions of Perron-Frobenius theorem will hold if it holds for the starting matrix of this family. Based on our observations, we develop a simple numerical technique...

A matrix is said to have the Perron-Frobenius property if 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 generalized nonnegative matrices are studied and certain topological aspects such as connectedness and closure are pro...

In a recent article, Bai and Perron (2003, Journal of Applied Econometrics) present a comprehensive discussion of computational aspects of multiple structural change models along with several empirical examples. Here, we report on the results of a replication study using the R statistical software package. We are able to verify most of their findings; however, some confidence intervals associat...

We generalize the Perron–Frobenius Theorem for nonnegative matrices to the class of nonnegative tensors.

A matrix is said to have the Perron-Frobenius property if 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 generalized nonnegative matrices are studied and certain topological aspects such as connectedness and closure are pro...

This article provides sufficient conditions for positive maps on the Schatten classes Jp; 1 p < 1 of bounded operators on a separable Hilbert space such that a corresponding Perron-Frobenius theorem holds. With applications in quantum information theory in mind sufficient conditions are given for a trace preserving, positive map on J1, the space of trace class operators, to have a unique, stric...

A parallel algorithm is presented for computing the group inverse of a singular M–matrix of the form A = I − T , where T ∈ Rn×n is irreducible and stochastic. The algorithm is constructed in the spirit of Meyer’s Perron complementation approach to computing the Perron vector of an irreducible nonnegative matrix. The asymptotic number of multiplication operations that is necessary to implement t...