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- Title
Determinants of Arrowhead Matrices over Finite Commutative Chain Rings.
- Authors
Jitman, Somphong; Modjam, Pornrudee
- Abstract
Arrowhead matrices have attracted attention due to their rich algebraic structures and numerous applications. In this paper, we focus on the enumeration of n × n arrowhead matrices with prescribed determinant over a finite field Fq and over a finite commutative chain ring R. The number of n×n arrowhead matrices over Fq of a fixed determinant a is determined for all positive integers n and for all elements a ∈ Fq. As applications, this result is used in the enumeration of n × n non-singular arrowhead matrices with prescribed determinant over R. Subsequently, some bounds on the number of n × n singular arrowhead matrices over R of a fixed determinant are given. Finally, some open problems are presented.
- Subjects
ARROWHEADS; DETERMINANTS (Mathematics); FINITE fields; MATRICES (Mathematics); NOETHERIAN rings
- Publication
European Journal of Pure & Applied Mathematics, 2024, Vol 17, Issue 1, p11
- ISSN
1307-5543
- Publication type
Article
- DOI
10.29020/nybg.ejpam.v17i1.4983