On the some properties of circulant matrix with third order linear recurrent sequence

TL;DR

This paper explores properties of circulant matrices constructed from third order linear recurrent sequences, specifically Van Der Laan, Cordonnier, and Perrin numbers, including eigenvalues, spectral norms, and determinants.

Contribution

It introduces a systematic analysis of circulant matrices based on third order linear recurrent sequences and derives explicit formulas for their eigenvalues, norms, and determinants.

Findings

Eigenvalues of circulant matrices with these sequences are explicitly computed.

Spectral norms and determinants are derived for matrices with Van Der Laan, Cordonnier, and Perrin numbers.

Properties of the sequences are used to generalize matrix characteristics.

Abstract

In this paper, firstly, we give the some fundamental properties of Van Der Laan numbers. After, we define the circulant matrices C(Z) which entries is third order linear recurrent sequence. In addition, we compute eigenvalues, spectral norm and determinant of this matrix. Consequently, by using properties of this sequence, we obtain the eigenvalues, norms and determinants of circulant matrices with Cordonnier, Perrin and Van Der Laan numbers.