The principal rank characteristic sequence over various fields

Date
2014-10-15
Authors
Barrett, Wayne
Butler, Steve
Catral, Minerva
Hogben, Leslie
Fallat, Shaun
Hall, H. Tracy
Hogben, Leslie
van den Driessche, P.
Young, Michael
Major Professor
Advisor
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
Altmetrics
Authors
Research Projects
Organizational Units
Mathematics
Organizational Unit
Journal Issue
Series
Department
Electrical and Computer EngineeringMathematics
Abstract

Given an n x n matrix, its principal rank characteristic sequence is a sequence of length n+1 of 0s and 1s where, for k = 0, 1, . . . , n, a 1 in the kth position indicates the existence of a principal submatrix of rank k and a 0 indicates the absence of such a submatrix. The principal rank characteristic sequences for symmetric matrices over various fields are investigated, with all such attainable sequences determined for all n over any field with characteristic 2. A complete list of attainable sequences for real symmetric matrices of order 7 is reported.

Comments

This is a manuscript of an article published as Barrett, Wayne, Steve Butler, Minerva Catral, Shaun M. Fallat, H. Tracy Hall, Leslie Hogben, Pauline van den Driessche, and Michael Young. "The principal rank characteristic sequence over various fields." Linear Algebra and its Applications 459 (2014): 222-236. DOI: 10.1016/j.laa.2014.06.045. Posted with permission.

Description
Keywords
Citation
DOI
Collections