On the spectral and Frobenius norm of a generalized Fibonacci r-circulant matrix
Special Matrices, 2018 Consider the recursion g0 = a, g1 = b, gn = gn−1 + gn−2, n = 2, 3, . . . . We compute the Frobenius norm of the r-circulant matrix corresponding to g0, . . . , gn−1. We also give three lower bounds (with equality conditions) for the spectral norm of this
Merikoski Jorma K. +3 more
doaj +8 more sources
A New Method of Matrix Decomposition to Get the Determinants and Inverses of r-Circulant Matrices with Fibonacci and Lucas Numbers [PDF]
Journal of Mathematics, 2021 We use a new method of matrix decomposition for r-circulant matrix to get the determinants of An=CircrF1,F2,…,Fn and Bn=CircrL1,L2,…,Ln, where Fn is the Fibonacci numbers and Ln is the Lucas numbers.
Jiangming Ma, Tao Qiu, Chengyuan He
doaj +2 more sources
Exact Recursive Calculation of Circulant Permanents: A Band of Different Diagonals inside a Uniform Matrix [PDF]
Entropy, 2021 V V Kocharovsky +2 more
exaly +2 more sources
On the Properties of r-Circulant Matrices Involving Generalized Fermat Numbers
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2023 -circulant matrices have applied in numerical computation, signal processing, coding theory, etc. In this study, our main goal is to investigate the r-circulant matrices of generalized Fermat numbers which are shown by We obtain the eigenvalues ...
Engin Özkan, Engin Eser, Bahar Kuloǧlu
doaj +1 more source
The Pseudoinverse of an r-Circulant Matrix [PDF]
Proceedings of the American Mathematical Society, 1972 It is shown that the Moore-Penrose pseudoinverse C + {C^ + }
Stallings, W. T., Boullion, T. L.
openaire +2 more sources
On the norms of an r-circulant matrix with the generalized k-Horadam numbers [PDF]
Journal of Inequalities and Applications, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yazlik, Yasin, Taskara, Necati
openaire +1 more source
Cluster solutions in networks of weakly coupled oscillators on a 2D square torus
Mathematics in Applied Sciences and Engineering, 2021 We consider a model for an N × N lattice network of weakly coupled neural oscilla- tors with periodic boundary conditions (2D square torus), where the coupling between neurons is assumed to be within a von Neumann neighborhood of size r, denoted as von ...
Jordan Michael Culp
doaj +1 more source
Representations of group rings and groups [PDF]
International Journal of Group Theory, 2018 An isomorphism between the group ring of a finite group and a ring of certain block diagonal matrices is established. It is shown that for any group ring matrix $A$ of $mathbb{C} G$ there exists a matrix $U$ (independent of $A$) such that $U^{-1}AU= diag(
Ted Hurley
doaj +1 more source
On the spectral norms of some circulant matrices with the trigonometric functions
Journal of Inequalities and Applications, 2019 In this paper, we use the properties of an r-circulant matrix and a geometric circulant matrix to study the spectral norms of the r-circulant matrix and the geometric circulant matrix involving trigonometric functions by some algebra methods.
Baijuan Shi
doaj +1 more source
More Constructions of Light MDS Transforms Based on Known MDS Circulant Matrices
Information, 2022 Maximum distance separable (MDS) codes have the maximum branch number in cryptography, and they are generally used in diffusion layers of symmetric ciphers.
Jin-Bo Wang, You Wu, Yu Zhou
doaj +1 more source