The numerical range of matrices over F4F4\mathbb {F}_4

Edoardo BALLICO

Article Details

The numerical range of matrices over F4F4\mathbb {F}_4

Authors:

Edoardo BALLICO

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2019 Vol.43 Issue 2, pp.955-964

Document Type:

Article

Publication Date:

3/2019

Document Language:

Turkish

Document ID (Org No.):

2000745660

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098

Abstract:

 

For any prime power qqq and any u=(x1,…,xn),v=(y1,…,yn)∈Fnq2u=(x1,…,xn),v=(y1,…,yn)∈Fq2nu = (x_1,\dots ,x_n),v = (y_1,\dots ,y_n)\in \mathbb {F} _{q^2}^n set  ⟨u,v⟩:=∑ni=1xqiyi⟨u,v⟩:=∑i=1nxiqyi\langle u,v\rangle := \sum _{i=1}^{n} x_i^qy_i. For any k∈Fqk∈Fqk\in \mathbb {F} _q and any n×nn×nn\times n matrix MMM over Fq2Fq2\mathbb {F} _{q^2}, the  kkk-numerical range Numk(M)Numk(M)\mathrm{Num} _k(M) of MMM is the set of all ⟨u,Mu⟩⟨u,Mu⟩\langle u,Mu\rangle for u∈Fnq2u∈Fq2nu\in \mathbb {F} _{q^2}^n with ⟨u,u⟩=k⟨u,u⟩=k\langle  u,u\rangle =k \cite{cjklr}. Here, we study the case q=2q=2q=2, which is  quite different from the case q≠2q≠2q\ne 2.

Article Details

The numerical range of matrices over F4F4\mathbb {F}_4

Authors: Edoardo BALLICO

Publisher: TUBITAK

Journal: Turkish Journal of Mathematics 2019 Vol.43 Issue 2, pp.955-964

Document Type: Article

Publication Date: 3/2019

Document Language: Turkish

Document ID (Org No.): 2000745660

Frequency: Bimonthly

eISSN: 1303-6149

pISSN: 1300-0098

Issues

Authors:

Edoardo BALLICO

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2019 Vol.43 Issue 2, pp.955-964

Document Type:

Article

Publication Date:

3/2019

Document Language:

Turkish

Document ID (Org No.):

2000745660

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098