Campus Units

Mathematics

Document Type

Article

Publication Version

Published Version

Publication Date

2-2017

Journal or Book Title

Electronic Journal of Linear Algebra

Volume

32

First Page

58

Last Page

75

DOI

10.13001/1081-3810.3249

Abstract

The enhanced principal rank characteristic sequence (epr-sequence) of an n x n matrix is a sequence l(1) l(2) . . .l(n), where each l(k) is A, S, or N according as all, some, or none of its principal minors of order k are nonzero. There has been substantial work on epr-sequences of symmetric matrices (especially real symmetric matrices) and real skew-symmetric matrices, and incidental remarks have been made about results extending (or not extending) to (complex) Hermitian matrices. A systematic study of epr-sequences of Hermitian matrices is undertaken; the differences with the case of symmetric matrices are quite striking. Various results are established regarding the attainability by Hermitian matrices of epr-sequences that contain two Ns with a gap in between. Hermitian adjacency matrices of mixed graphs that begin with N A N are characterized. All attainable epr-sequences of Hermitian matrices of orders 2, 3, 4, and 5, are listed with justifications.

Comments

This article is published as Butler, Steve, Minerva Catral, H. Tracy Hall, Leslie Hogben, Xavier Martinez-Rivera, Bryan Shader, and Pauline Van Den Driessche. "The enhanced principal rank characteristic sequence for Hermitian matrices." The Electronic Journal of Linear Algebra 32 (2017): 58-75. DOI: 10.13001/1081-3810.3249. Posted with permission.

Copyright Owner

The Author(s)

Language

en

File Format

application/pdf

Included in

Algebra Commons

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