Open Accessm-NIL-CLEAN COMPANION MATRICES
Author(s) -
Andrada Cîmpean
Publication year - 2019
Publication title -
the electronic journal of linear algebra
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.447
H-Index - 31
eISSN - 1537-9582
pISSN - 1081-3810
DOI - 10.13001/ela.2019.4937
Subject(s) - mathematics , trace (psycholinguistics) , dimension (graph theory) , nilpotent , pure mathematics , matrix (chemical analysis) , prime (order theory) , companion matrix , combinatorics , algebra over a field , mathematical analysis , philosophy , linguistics , materials science , matrix polynomial , polynomial matrix , polynomial , composite material
Companion matrices over fields of prime characteristic, p, that are sums of two idempotents and a nilpotent are characterized in terms of dimension and trace of such a matrix and of p. Companion matrices over fields of positive characteristic, p, that are sums of m idempotents, m ≥ 2, and a nilpotent are characterized in terms of dimension and trace of such a matrix and of p.