Determinants of Circulant Matrices with Some Certain Sequences
Ercan Alt{\i}n{\i}\c{s}{\i}k
TL;DR
This paper derives a general formula for the determinants of circulant matrices generated by sequences satisfying linear recurrence relations, extending previous specific cases.
Contribution
It provides a unified determinant formula for circulant matrices from sequences defined by linear recurrence relations, generalizing earlier results.
Findings
Derived a determinant formula for circulant matrices with recurrence-defined sequences
Extended previous specific determinant results to a general case
Provides a mathematical tool for analyzing circulant matrices in related fields
Abstract
Let be a sequence of real numbers defined by an th order linear homogenous recurrence relation. In this paper we obtain a determinant formula for the circulant matrix , providing a generalization of determinantal results in papers of Bozkurt \cite{Bozkurt}, Bozkurt and Tam \cite{BozkurtTam}, and Shen, et al. \cite{ShenCenHao}.
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Mathematical Theories and Applications · Graph theory and applications