On Matrices with Perron–Frobenius Properties and Some Negative Entries

On Matrices with Perron–Frobenius Properties and Some Negative Entries We consider those n-by-n matrices with a strictly dominant positive eigenvalue of multiplicity 1 and associated positive left and right eigenvectors. Such matrices may have negative entries and generalize the primitive matrices in important ways. Several ways of constructing such matrices, including a very geometric one, are discussed. This paper grew out of a recent survey talk about nonnegative matrices by the first author and a joint paper, with others, by the second author about the symmetric case [Tarazaga et al. (2001) Linear Algebra Appl. 328: 57]. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

On Matrices with Perron–Frobenius Properties and Some Negative Entries

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2004 by Kluwer Academic Publishers
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-003-3881-3
Publisher site
See Article on Publisher Site

Abstract

We consider those n-by-n matrices with a strictly dominant positive eigenvalue of multiplicity 1 and associated positive left and right eigenvectors. Such matrices may have negative entries and generalize the primitive matrices in important ways. Several ways of constructing such matrices, including a very geometric one, are discussed. This paper grew out of a recent survey talk about nonnegative matrices by the first author and a joint paper, with others, by the second author about the symmetric case [Tarazaga et al. (2001) Linear Algebra Appl. 328: 57].

Journal

PositivitySpringer Journals

Published: Mar 2, 2003

References

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