Eventually nonnegative matrices are similar to seminonnegative matrices

In this paper, it is shown that the necessary and sufficient conditions on the Jordan form of a seminonnegative matrix, identified by Zaslavsky and McDonald, are in fact necessary and sufficient conditions on the Jordan form of every eventually nonnegative matrix. Thus every eventually nonnegative m...

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Bibliographic Details
Published in:Linear algebra and its applications Vol. 381; pp. 245 - 258
Main Authors: Carnochan Naqvi, Sarah, McDonald, Judith J.
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 01.04.2004
Elsevier Science
Subjects:
Algebra
Eventually nonnegative matrices
Exact sciences and technology
Height characteristic
Index of cyclicity
Jordan form
Level characteristic
Linear and multilinear algebra, matrix theory
Mathematics
Sciences and techniques of general use
Seminonnegative matrices
Height characteristic
Level characteristic
Eventually nonnegative matrices
Seminonnegative matrices
Jordan form
Index of cyclicity
Non negative matrix
Necessary and sufficient condition
First order
Linear algebra
Irreducible operator
Index
Reliability
Jordan algebra
ISSN:0024-3795, 1873-1856
Online Access:Get full text
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Summary:In this paper, it is shown that the necessary and sufficient conditions on the Jordan form of a seminonnegative matrix, identified by Zaslavsky and McDonald, are in fact necessary and sufficient conditions on the Jordan form of every eventually nonnegative matrix. Thus every eventually nonnegative matrix is similar to a seminonnegative matrix. In [Linear Algebra Appl. 372 (2003) 253], they show that several of the combinatorial properties of reducible nonnegative matrices carry over to reducible seminonnegative matrices. In this paper it is shown that a property on the index of cyclicity of an irreducible nonnegative matrix carries over to the seminonnegative matrices.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2003.11.021