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Determinants of Arrowhead Matrices over Finite Commutative Chain Rings.
- Source :
-
European Journal of Pure & Applied Mathematics . Jan2024, Vol. 17 Issue 1, p11-29. 19p. - Publication Year :
- 2024
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 13075543
- Volume :
- 17
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- European Journal of Pure & Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 175587702
- Full Text :
- https://doi.org/10.29020/nybg.ejpam.v17i1.4983