The numerical range of matrices over F4

Abstract

For any prime power q and any u = (x , . . . , x ), v = (y , . . . , y ) ∈ Fnset ⟨u, v⟩ := ∑nxqy . For anyk ∈ F and any n × n matrix M over Fq2 , the k -numerical range Num (M ) of M is the set of all ⟨u, Mu⟩ for u ∈ Fnwith ⟨u, u⟩ = k [5]. Here, we study the case q = 2 , which is quite different from the case q ̸= 2 .