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Jordan Structures of Totally Nonnegative Matrices

Published online by Cambridge University Press:  20 November 2018

Shaun M. Fallat  and
Michael I. Gekhtman
Shaun M. Fallat
Affiliation:
Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan, S4S 0A2 e-mail: sfallat@math.uregina.ca
Michael I. Gekhtman
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, IN. 46556-5683 U.S.A. e-mail: Michael.Gekhtman.1@nd.edu
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Abstract

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An $n\times n$ matrix is said to be totally nonnegative if every minor of $A$ is nonnegative. In this paper we completely characterize all possible Jordan canonical forms of irreducible totally nonnegative matrices. Our approach is mostly combinatorial and is based on the study of weighted planar diagrams associated with totally nonnegative matrices.

Keywords

15A2115A4805C38totally nonnegativematricesplanar diagramsprincipal rankJordan canonical form
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 57 , Issue 1 , 01 February 2005 , pp. 82 - 98
Copyright
Copyright © Canadian Mathematical Society 2005

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