Improved tests and characterizations of totally nonnegative matrices

2014
Journal article
Published in
Electronic Journal of Linear Algebra (ELA) ; 27 (2014). - pp. 588-610. - ISSN 1081-3810. - eISSN 1537-9582
Abstract
Totally nonnegative matrices, i.e., matrices having all minors nonnegative, are considered. A condensed form of the Cauchon algorithm which has been proposed for finding a parameterization of the set of these matrices with a fixed pattern of nonvanishing minors is derived. The close connection of this variant to Neville elimination and bidiagonalization is shown and new determinantal tests for total nonnegativity are developed which require much fever minors to be tested than for the tests known so far. New characterizations of some subclasses of the totally nonnegative matrices as well as shorter proofs for some classes of matrices for being (nonsingular and) totally nonnegative are derived.
510 Mathematics
Keywords
Totally nonnegative matix, totally positive matrix, Cauchon algorithm, Neville elimination, bidiagonalization
Cite This
ISO 690ADM, Mohammad, Jürgen GARLOFF, 2014. Improved tests and characterizations of totally nonnegative matrices. In: Electronic Journal of Linear Algebra (ELA). 27, pp. 588-610. ISSN 1081-3810. eISSN 1537-9582. Available under: doi: 10.13001/1081-3810.1920
BibTex
@article{Adm2014Impro-29987,
year={2014},
doi={10.13001/1081-3810.1920},
title={Improved tests and characterizations of totally nonnegative matrices},
url={http://repository.uwyo.edu/ela/vol27/iss1/255/},
volume={27},
issn={1081-3810},
journal={Electronic Journal of Linear Algebra (ELA)},
pages={588--610},
note={Article Number: 255}
}

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