scholarly journals On Skew Circulant Type Matrices Involving Any Continuous Fibonacci Numbers

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Zhaolin Jiang ◽  
Jinjiang Yao ◽  
Fuliang Lu
Keyword(s):  
Fibonacci Numbers ◽  
Spectral Norm ◽  
Matrix Norm ◽  
Circulant Matrices ◽  
Frobenius Norm ◽  
Transformation Matrices ◽  
Skew Circulant

Circulant and skew circulant matrices have become an important tool in networks engineering. In this paper, we consider skew circulant type matrices with any continuous Fibonacci numbers. We discuss the invertibility of the skew circulant type matrices and present explicit determinants and inverse matrices of them by constructing the transformation matrices. Furthermore, the maximum column sum matrix norm, the spectral norm, the Euclidean (or Frobenius) norm, and the maximum row sum matrix norm and bounds for the spread of these matrices are given, respectively.

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 The Determinants, Inverses, Norm, and Spread of Skew Circulant Type Matrices Involving Any Continuous Lucas Numbers

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Jin-jiang Yao ◽  
Zhao-lin Jiang
Keyword(s):  
Circulant Matrix ◽  
Circulant Matrices ◽  
Lucas Numbers ◽  
Transformation Matrices ◽  
Skew Circulant ◽  
The Relationship

We consider the skew circulant and skew left circulant matrices with any continuous Lucas numbers. Firstly, we discuss the invertibility of the skew circulant matrices and present the determinant and the inverse matrices by constructing the transformation matrices. Furthermore, the invertibility of the skew left circulant matrices is also discussed. We obtain the determinants and the inverse matrices of the skew left circulant matrices by utilizing the relationship between skew left circulant matrices and skew circulant matrix, respectively. Finally, the four kinds of norms and bounds for the spread of these matrices are given, respectively.

scholarly journals Explicit Euclidean Norm, Eigenvalues, Spectral Norm and Determinant of Circulant Matrix with the Generalized Tribonacci Numbers

2021 ◽  
pp. 131-151
Author(s):  
Yüksel Soykan
Keyword(s):  
Circulant Matrix ◽  
Spectral Norm ◽  
Matrix Norm ◽  
Circulant Matrices ◽  
Euclidean Norm ◽  
Hadamard Products ◽  
Tribonacci Numbers

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.

scholarly journals VanderLaan Circulant Type Matrices

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Hongyan Pan ◽  
Zhaolin Jiang
Keyword(s):  
Lower Bound ◽  
Complex Systems ◽  
Circulant Matrix ◽  
Spectral Norm ◽  
Circulant Matrices ◽  
Control Methods ◽  
Tridiagonal Matrices ◽  
Transformation Matrices

Circulant matrices have become a satisfactory tools in control methods for modern complex systems. In the paper, VanderLaan circulant type matrices are presented, which include VanderLaan circulant, left circulant, andg-circulant matrices. The nonsingularity of these special matrices is discussed by the surprising properties of VanderLaan numbers. The exact determinants of VanderLaan circulant type matrices are given by structuring transformation matrices, determinants of well-known tridiagonal matrices, and tridiagonal-like matrices. The explicit inverse matrices of these special matrices are obtained by structuring transformation matrices, inverses of known tridiagonal matrices, and quasi-tridiagonal matrices. Three kinds of norms and lower bound for the spread of VanderLaan circulant and left circulant matrix are given separately. And we gain the spectral norm of VanderLaang-circulant matrix.

scholarly journals Norms and Spread of the Fibonacci and Lucas RSFMLR Circulant Matrices

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Wenai Xu ◽  
Zhaolin Jiang
Keyword(s):  
Kronecker Product ◽  
Hadamard Product ◽  
Circulant Matrix ◽  
Spectral Norm ◽  
Circulant Matrices ◽  
Frobenius Norm

Circulant type matrices have played an important role in networks engineering. In this paper, firstly, some bounds for the norms and spread of Fibonacci row skew first-minus-last right (RSFMLR) circulant matrices and Lucas row skew first-minus-last right (RSFMLR) circulant matrices are given. Furthermore, the spectral norm of Hadamard product of a Fibonacci RSFMLR circulant matrix and a Lucas RSFMLR circulant matrix is obtained. Finally, the Frobenius norm of Kronecker product of a Fibonacci RSFMLR circulant matrix and a Lucas RSFMLR circulant matrix is presented.

scholarly journals On k-circulant matrices with the generalized third-order Pell numbers

2021 ◽  
Vol 27 (4) ◽  
pp. 187-206
Author(s):  
Yüksel Soykan ◽  
Keyword(s):  
Circulant Matrix ◽  
Numerical Results ◽  
Spectral Norm ◽  
Matrix Norm ◽  
Circulant Matrices ◽  
Euclidean Norm ◽  
Third Order ◽  
Pell Numbers

In this paper, we obtain explicit forms of the sum of entries, the maximum column sum matrix norm, the maximum row sum matrix norm, Euclidean norm, eigenvalues and determinant of k-circulant matrix with the generalized third-order Pell numbers. We also study the spectral norm of this k-circulant matrix. Furthermore, some numerical results for demonstrating the validity of the hypotheses of our results are given.

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