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Efficient Recognition of Totally Nonnegative Matrix Cells

Launois, Stephane, Lenagan, T.H. (2014) Efficient Recognition of Totally Nonnegative Matrix Cells. Foundations of Computational Mathematics, 14 (2). pp. 371-387. ISSN 1615-3375. (doi:10.1007/s10208-013-9169-5) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
Official URL
http://dx.doi.org/10.1007/s10208-013-9169-5

Abstract

The space of m×p totally nonnegative real matrices has a stratification into totally nonnegative cells. The largest such cell is the space of totally positive matrices. There is a well-known criterion due to Gasca and Peña for testing a real matrix for total positivity. This criterion involves testing mp minors. In contrast, there is no known small set of minors for testing for total nonnegativity. In this paper, we show that for each of the totally nonnegative cells there is a test for membership which only involves mp minors, thus extending the Gasca and Peña result to all totally nonnegative cells.

Item Type: Article
DOI/Identification number: 10.1007/s10208-013-9169-5
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Stephane Launois
Date Deposited: 09 May 2014 12:36 UTC
Last Modified: 15 Jan 2020 14:30 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/41059 (The current URI for this page, for reference purposes)
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