Open AccessThe numerical range of matrices over F4
Author(s) -
Edoardo Ballico
Publication year - 2019
Publication title -
turkish journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.454
H-Index - 27
eISSN - 1303-6149
pISSN - 1300-0098
DOI - 10.3906/mat-1810-100
Subject(s) - mathematics , combinatorics , prime power , prime (order theory) , range (aeronautics) , matrix (chemical analysis) , physics , chemistry , materials science , composite material , chromatography
For any prime power q and any u = (x1, . . . , xn), v = (y1, . . . , yn) ∈ Fnq2 set ⟨u, v⟩ := ∑n i=1 x q i yi . For any k ∈ Fq and any n×n matrix M over Fq2 , the k -numerical range Numk(M) of M is the set of all ⟨u,Mu⟩ for u ∈ Fnq2 with ⟨u, u⟩ = k [5]. Here, we study the case q = 2 , which is quite different from the case q ̸= 2 .
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