Abstract
In this paper, we obtain explicit Euclidean norm, eigenvalues, spectral norm and determinant of circulant matrix with the generalized Tribonacci (generalized (r, s, t)) numbers. We also present the sum of entries, the maximum column sum matrix norm and the maximum row sum matrix norm of this circulant matrix. Moreover, we give some bounds for the spectral norms of Kronecker and Hadamard products of circulant matrices of (r, s, t) and Lucas (r, s, t) numbers.
Reference53 articles.
1. E. Alptekin and G. Pell, Pell-Lucas ve Modified Pell sayıları ile tanımlı circulant ve semicirculant matrisler, Doctoral dissertation, Selçuk Üniversitesi Fen Bilimleri Enstitüsü, 2005.
2. I. Bruce, A modified Tribonacci sequence, Fibonacci Quart. 22(3) (1984), 244-246.
3. M. Catalani, Identities for Tribonacci-related sequences, 2012. arXiv:math/0209179
4. E. Choi, Modular Tribonacci numbers by matrix method, J. Korean Soc. Math. Educ. Ser. B Pure Appl. Math. 20(3) (2013), 207-221. https://doi.org/10.7468/jksmeb.2013.20.3.207
5. R.E. Cline, R.J. Plemmons and G. Worm, Generalized inverses of certain Toeplitz matrices, Linear Algebra Appl. 8 (1974), 25-33. https://doi.org/10.1016/0024-3795(74)90004-4