The enhanced principal rank characteristic sequence for skew-symmetric matrices

Date
2015-08-15
Authors
Fallat, Shaun
Olesky, Dale
van den Driessche, Pauline
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Abstract

The enhanced principal rank characteristic sequence (epr-sequence) was originally defined for an n ×n real symmetric matrix or an n ×n Hermitian matrix. Such a sequence is defined to be l1l2···ln where lk is A,S, or N depending on whether all, some, or none of the matrix principal minors of order k are nonzero. Here we give a complete characterization of the attainable epr-sequences for real skew-symmetric matrices. With the constraint that lk=0 if k is odd, we show that nearly all epr-sequences are attainable by skew-symmetric matrices, which is in contrast to the case of real symmetric or Hermitian matrices for which many epr-sequences are forbidden. ©2015

Description
Keywords
principal rank, skew-symmetric matrix, minor, rank
Citation
http://dx.doi.org/10.1016/j.laa.2015.08.014
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