On the geometry of numerical ranges over finite fields

Numerical ranges over a certain family of finite fields were classified in 2016 by a team including our fifth author [5]. Soon afterward Ballico generalized these results to all finite fields and published some new results about the cardinality of the finite field numerical range [1,2]. In this pape...

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Bibliographic Details
Published in:Linear algebra and its applications 2021-11, Vol.628, p.182-201
Main Authors: Camenga, Kristin A., Collins, Brandon, Hoefer, Gage, Quezada, Jonny, Rault, Patrick X., Willson, James, Yates, Rebekah B. Johnson
Format: Article
Language:English
Subjects:
[formula omitted] matrices
Binary system
Boundary generating curve
Eigenvalues
Field of values
Fields (mathematics)
Finite fields
Linear algebra
Numbers
Numerical range
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Summary:Numerical ranges over a certain family of finite fields were classified in 2016 by a team including our fifth author [5]. Soon afterward Ballico generalized these results to all finite fields and published some new results about the cardinality of the finite field numerical range [1,2]. In this paper we study the geometry of these finite fields using the boundary generating curve, first introduced by Kippenhahn in 1951 [8,9]. We restrict our study to square matrices of dimension 2, with at least one eigenvalue in Fq2.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2021.07.008