On r-circulant matrices with Fibonacci and Lucas numbers having arithmetic indices

2017 ◽  
Author(s):  
Aldous Cesar F. Bueno
Keyword(s):  
Circulant Matrices ◽  
Lucas Numbers ◽  
Fibonacci And Lucas Numbers

scholarly journals A New Method of Matrix Decomposition to Get the Determinants and Inverses of r -Circulant Matrices with Fibonacci and Lucas Numbers

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Jiangming Ma ◽  
Tao Qiu ◽  
Chengyuan He
Keyword(s):  
Fibonacci Numbers ◽  
Matrix Decomposition ◽  
Circulant Matrix ◽  
New Method ◽  
Circulant Matrices ◽  
Computational Time ◽  
Lucas Numbers ◽  
Fibonacci And Lucas Numbers

We use a new method of matrix decomposition for r -circulant matrix to get the determinants of A n = Circ r F 1 , F 2 , … , F n and B n = Circ r L 1 , L 2 , … , L n , where F n is the Fibonacci numbers and L n is the Lucas numbers. Based on these determinants and the nonsingular conditions, inverse matrices are derived. The expressions of the determinants and inverse matrices are represented by Fibonacci and Lucas Numbers. In this study, the formulas of determinants and inverse matrices are much simpler and concise for programming and reduce the computational time.

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

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Zhaolin Jiang ◽  
Yunlan Wei
Keyword(s):  
Differential Equations ◽  
Research Area ◽  
Spectral Norm ◽  
Matrix Norm ◽  
Circulant Matrices ◽  
Frobenius Norm ◽  
Lucas Numbers ◽  
Skew Circulant ◽  
Fibonacci And Lucas Numbers

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.

scholarly journals On the determinants and inverses of R-circulant matrices with the biperiodic Fibonacci and Lucas numbers

Filomat ◽  
2018 ◽  
Vol 32 (10) ◽  
pp. 3637-3650 ◽  
Author(s):  
Cahit Köme ◽  
Yasin Yazlik
Keyword(s):  
Circulant Matrices ◽  
Lucas Numbers ◽  
Fibonacci And Lucas Numbers

In this paper, we present a new generalization to compute determinants and inverses of r-circulant matrices Qn = circr ((b/a)?(2)/2 q1,(b/a)?(3)/2 q2,..., (b/a)?(n+1)/2 qn) and Ln = circr ((b/a)?(1)/2 l1,(b/a)?(2)/2 l2,..., (b/a)?(n)/2 ln) whose entries are the biperiodic Fibonacci and the biperiodic Lucas numbers, respectively. Also, we express determinants of the matrices Qn and Ln by using only the biperiodic Fibonacci and the biperiodic Lucas numbers.

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