A note on minimum rank and maximum nullity of sign patterns

Thumbnail Image
Date
2011-03-01
Authors
Hogben, Leslie
Major Professor
Advisor
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
Authors
Person
Hogben, Leslie
Associate Dean
Research Projects
Organizational Units
Organizational Unit
Mathematics
Welcome to the exciting world of mathematics at Iowa State University. From cracking codes to modeling the spread of diseases, our program offers something for everyone. With a wide range of courses and research opportunities, you will have the chance to delve deep into the world of mathematics and discover your own unique talents and interests. Whether you dream of working for a top tech company, teaching at a prestigious university, or pursuing cutting-edge research, join us and discover the limitless potential of mathematics at Iowa State University!
Journal Issue
Is Version Of
Versions
Series
Department
Mathematics
Abstract

The miminum rank of a sign pattern matrix is defined to be the smallest possible rank over all real matrices having the given sign pattern. The maximum nullity of a sign pattern is the largest possible nullity over the same set of matrices, and is equal to the number of columns minus the minimum rank of the sign pattern. Definitions of various graph parameters that have been used to bound maximum nullity of a zero-nonzero pattern, including path cover number and edit distacnce, are extended to sign patterns, and the SNS number is introduced to usefully generalized the triangle number to sign patterns. It is shown number, and maximum nullity, path cover number and edit distance are equal, providing a method to compute minimum rank for tree sign patterns. The minimum rank of small sign patterns is determined.

Comments

This article is published as Hogben, Leslie. "A note on minimum rank and maximum nullity of sign patterns." The Electronic Journal of Linear Algebra 22 (2011): 203-213. DOI: 10.13001/1081-3810.1435. Posted with permission.

Description
Keywords
Citation
DOI
Subject Categories
Copyright
Sat Jan 01 00:00:00 UTC 2011
Collections