Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4598401 | Linear Algebra and its Applications | 2017 | 10 Pages |
Abstract
Let q be a prime power. Following a paper by Coons, Jenkins, Knowles, Luke and Rault (case q a prime p≡3(mod4)) we define the numerical range Num(M)⊆Fq2Num(M)⊆Fq2 of an n×nn×n-matrix M with coefficients in Fq2Fq2 in terms of the usual Hermitian form. We prove that ♯(Num(M))>q♯(Num(M))>q (case q≠2q≠2), unless M is unitarily equivalent to a diagonal matrix with eigenvalues contained in an affine FqFq-line. We study in details Num(M)Num(M) when n=2n=2.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
E. Ballico,