On the some properties of circulant matrices with third order linear recurrent sequences. (English) Zbl 1407.11045

Coskun, Arzu; Taskara, Necati

Math. Sci. Appl. E-Notes 6, No. 1, 12-18 (2018).

Summary: 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 are third order linear recurrent sequences. 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.

MSC:

11C20	Matrices, determinants in number theory
15A15	Determinants, permanents, traces, other special matrix functions
11B50	Sequences (mod \(m\))

Keywords:

third order linear recurrent sequence; Cordonnier numbers; Perrin numbers; Van der Laan numbers; circulant matrix