Campus Units
Mathematics, Electrical and Computer Engineering
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.
Copyright Owner
The Author(s)
Copyright Date
2017
Language
en
File Format
application/pdf
Recommended Citation
Butler, Steve; Catral, Minerva; Hall, H. Tracy; Hogben, Leslie; Martinez-Rivera, Xavier; Shader, Bryan L.; and van den Driessche, Pauline, "The Enhanced Principal Rank Characteristic Sequence for Hermitian Matrices" (2017). Mathematics Publications. 233.
https://lib.dr.iastate.edu/math_pubs/233
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.