Work

Sign patterns that allow strong eventual nonnegativity

Year: 2012

Type: article

Abstract: A new class of sign patterns contained in the class of sign patterns that allow eventual nonnegativity is introduced and studied.A sign pattern is potentially strongly eventually nonnegative (PSEN) if there is a matrix with this sign pattern that is eventually nonnegative and has some power that is both nonnegative and irreducible.Using Perron-Frobenius theory and a matrix perturbation result, it is proved that a PSEN sign pattern is either potentially eventually positive or r-cyclic.The minimum number of positive entries in an n × n PSEN sign pattern is shown to be n, and PSEN sign patterns of orders 2 and 3 are characterized.

Source: Electronic Journal of Linear Algebra

DOI: 10.13001/1081-3810.1502

Authors: M. Catral, C. Erickson, L. Hogben, D. Olesky, P. Van den Driessche

Institutions: Xavier University, Iowa State University, University of Victoria, American Institute of Mathematics

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funders: National Science Foundation, Banff International Research Station for Mathematical Innovation and Discovery, Natural Sciences and Engineering Research Council of Canada

Award: EMSW21-MCTP: Alliance for the Production of African American Ph.D.s in the Mathematical Sciences