Campus Units

Mathematics, Electrical and Computer Engineering

Document Type

Report

Conference

Banff International Research Station: Eventually Nonnegative Matrices and their Sign Patterns

Publication Version

Published Version

Link to Published Version

http://www.birs.ca/events/2011/focussed-research-groups/11frg149

Publication Date

2011

Conference Title

Banff International Research Station: Eventually Nonnegative Matrices and their Sign Patterns

Conference Date

May 15-22, 2011

City

Banff, Alberta, CA

Abstract

A matrix A ∈ R n×n is eventually nonnegative (respectively, eventually positive) if there exists a positive integer k0 such that for all k ≥ k0, Ak ≥ 0 (respectively, Ak > 0). Here inequalities are entrywise and all matrices are real and square. An eigenvalue of A is dominant if its magnitude is equal to the spectral radius of A. A matrix A has the strong Perron-Frobenius property if A has a unique dominant eigenvalue that is positive, simple, and has a positive eigenvector. It is well known (see, e.g., [10]) that the set of matrices for which both A and AT have the strong Perron-Frobenius property coincides with the set of eventually positive matrices. Eventually nonnegative matrices and eventually positive matrices have applications to positive control theory (see, e.g., [13]).

Comments

This is a report that resulted from the Banff International Research Station Focused Research Group and is published as Catral, Minerva, Craig Erickson, Leslie Hogben, D. D. Olesky, and P. van den Driessche. "Eventually Nonnegative Matrices and their Sign Patterns." Banff International Research Station: Eventually Nonnegative Matrices and their Sign Patterns, 2011. Posted with permission.

Copyright Owner

Banff International Research Station

Language

en

File Format

application/pdf

Published Version

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Article Location

 
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