Paper Info
Title
On the numerical range of matrices defined over a finite field
Abstract
Let q be a prime power. For u=(u1,…,un),v=(v1,…,vn)∈Fq2n let 〈u,v〉:=∑i=1nuiqvi be the Hermitian form of Fq2n. Fix an n×n matrix M over Fq2. Set Num(M):={〈u,Mu〉|u∈Fq2n,〈u,u〉=1} (the numerical range of M introduced by Coons, Jenkins, Knowles, Luke and Rault (case q a prime q≡3(mod4)) and by the author (arbitrary q)). When n=2 we prove an upper bound for |Num(M)|. We describe Num(M) for several classes of matrices, mostly for n=2,4.
Year
DOI
Venue
2020
10.1016/j.ffa.2020.101730
Finite Fields and Their Applications
Keywords
DocType
Volume
15A33,15A60,12E20
Journal
67
ISSN
Citations 
PageRank 
1071-5797
0
0.34
References 
Authors
0
1
Name
Order
Citations
PageRank
Edoardo Ballico1167.15