Campus Units

Mathematics, Electrical and Computer Engineering

Document Type

Article

Publication Version

Accepted Manuscript

Publication Date

6-1-2016

Journal or Book Title

Linear Algebra and its Applications

Volume

498

First Page

181

Last Page

200

DOI

10.1016/j.laa.2015.03.023

Abstract

The enhanced principal rank characteristic sequence (epr-sequence) of a symmetric n×n matrix is a sequence ℓ12⋯ℓn where ℓk is A, S, or N according as all, some, or none of its principal minors of order k are nonzero. Such sequences give more information than the (0,1) pr-sequences previously studied (where basically the kth entry is 0 or 1 according as none or at least one of its principal minors of order k is nonzero). Various techniques including the Schur complement are introduced to establish that certain subsequences such as NAN are forbidden in epr-sequences over fields of characteristic not two. Using probabilistic methods over fields of characteristic zero, it is shown that any sequence of As and Ss ending in A is attainable, and any sequence of As and Ss followed by one or more Ns is attainable; additional families of attainable epr-sequences are constructed explicitly by other methods. For real symmetric matrices of orders 2, 3, 4, and 5, all attainable epr-sequences are listed with justifications.

Comments

This is a manuscript of an article published as Butler, Steve, Minerva Catral, Shaun M. Fallat, H. Tracy Hall, Leslie Hogben, Pauline van den Driessche, and Michael Young. "The enhanced principal rank characteristic sequence." Linear Algebra and its Applications 498 (2016): 181-200. DOI: 10.1016/j.laa.2015.03.023. Posted with permission.

Copyright Owner

Elsevier Inc.

Language

en

File Format

application/pdf

Published Version

Share

COinS