A Characterization of Positive Matrices

A Characterization of Positive Matrices It is shown that an n-by-n matrix has a strictly dominant positive eigenvalue with positive left and right eigenvectors and this property is inherited by principle submatrices if and only if it is entry-wise positive. This limits the extent to which attractive Perron-Frobenius properities may be generalized outside the positive matrices. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

A Characterization of Positive Matrices

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2005 by Springer
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/s11117-005-7076-y
Publisher site
See Article on Publisher Site

Abstract

It is shown that an n-by-n matrix has a strictly dominant positive eigenvalue with positive left and right eigenvectors and this property is inherited by principle submatrices if and only if it is entry-wise positive. This limits the extent to which attractive Perron-Frobenius properities may be generalized outside the positive matrices.

Journal

PositivitySpringer Journals

Published: Mar 29, 2005

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