Circulant Type Matrices with the Sum and Product of Fibonacci and Lucas Numbers (original) (raw)

Skew Circulant Type Matrices Involving the Sum of Fibonacci and Lucas Numbers

Abstract and Applied Analysis, 2015

Skew circulant and circulant matrices have been an ideal research area and hot issue for solving various differential equations. In this paper, the skew circulant type matrices with the sum of Fibonacci and Lucas numbers are discussed. The invertibility of the skew circulant type matrices is considered. The determinant and the inverse matrices are presented. Furthermore, the maximum column sum matrix norm, the spectral norm, the Euclidean (or Frobenius) norm, the maximum row sum matrix norm, and bounds for the spread of these matrices are given, respectively.

A generalization of Fibonacci and Lucas matrices

Discrete Applied Mathematics, 2008

We define the matrix U (a,b,s) n of type s, whose elements are defined by the general second-order non-degenerated sequence and introduce the notion of the generalized Fibonacci matrix F (a,b,s) n , whose nonzero elements are generalized Fibonacci numbers. We observe two regular cases of these matrices (s = 0 and s = 1). Generalized Fibonacci matrices in certain cases give the usual Fibonacci matrix and the Lucas matrix. Inverse of the matrix U (a,b,s) n is derived. In partial case we get the inverse of the generalized Fibonacci matrix F

Gaussian Fibonacci Circulant Type Matrices

Abstract and Applied Analysis, 2014

Circulant matrices have become important tools in solving integrable system, Hamiltonian structure, and integral equations. In this paper, we prove that Gaussian Fibonacci circulant type matrices are invertible matrices for > 2 and give the explicit determinants and the inverse matrices. Furthermore, the upper bounds for the spread on Gaussian Fibonacci circulant and left circulant matrices are presented, respectively.

Determinants, inverses, norms, and spreads of skew circulant matrices involving the product of Fibonacci and Lucas numbers

Journal of Mathematics and Computer Science

In this paper, we investigate the invertibility of n × n skew circulant matrix involving the product of Fibonacci and Lucas numbers, whose determinant and inverse can be expressed by the (n − 1) th , n th , (n + 1) th , (n + 2) th product of Fibonacci and Lucas numbers. Some norms and bounds for the spread of these matrices are given, respectively. In addition, we generalize these results to skew left circulant matrix involving the product of Fibonacci and Lucas numbers. Finally, several numerical examples are illustrated to show the effectiveness of our theoretical results.

Explicit Form of the Inverse Matrices of Tribonacci Circulant Type Matrices

Abstract and Applied Analysis, 2015

It is a hot topic that circulant type matrices are applied to networks engineering. The determinants and inverses of Tribonacci circulant type matrices are discussed in the paper. Firstly, Tribonacci circulant type matrices are defined. In addition, we show the invertibility of Tribonacci circulant matrix and present the determinant and the inverse matrix based on constructing the transformation matrices. By utilizing the relation between left circulant, -circulant matrices and circulant matrix, the invertibility of Tribonacci left circulant and Tribonacci -circulant matrices is also discussed. Finally, the determinants and inverse matrices of these matrices are given, respectively.

On The Circulant K–Fibonacci Matrices

We started looking for a formula to simplify the calculation of the difference of two k–Fibonacci numbers depending on the kind of subscripts. Then we study the value of the determinant of circulant matrices whose entries are k–Fibonacci numbers. We continue calculating their eigenvalues and finish with the calculation of the eigenvalues of the matrix obtained multiplying the k–Fibonacci