Turkish Journal of Mathematics
DOI
10.3906/mat-1810-100
Abstract
For any prime power $q$ and any $u = (x_1,\dots ,x_n),v = (y_1,\dots ,y_n)\in \mathbb {F} _{q^2}^n$ set $\langle u,v\rangle := \sum _{i=1}^{n} x_i^qy_i$. For any $k\in \mathbb {F} _q$ and any $n\times n$ matrix $M$ over $\mathbb {F} _{q^2}$, the $k$-numerical range $\mathrm{Num} _k(M)$ of $M$ is the set of all $\langle u,Mu\rangle$ for $u\in \mathbb {F} _{q^2}^n$ with $\langle u,u\rangle =k$ \cite{cjklr}. Here, we study the case $q=2$, which is quite different from the case $q\ne 2$.
Keywords
numerical range, finite field, binary field
First Page
955
Last Page
964
Recommended Citation
BALLICO, EDOARDO
(2019)
"The numerical range of matrices over $\mathbb {F}_4$,"
Turkish Journal of Mathematics: Vol. 43:
No.
2, Article 27.
https://doi.org/10.3906/mat-1810-100
Available at:
https://journals.tubitak.gov.tr/math/vol43/iss2/27
