On Skew Circulant Type Matrices Involving Any Continuous Fibonacci Numbers

Zhaolin Jiang,Fuliang Lu,Jinjiang Yao

doi:10.1155/2014/483021

Abstract

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.

Highlights

Skew circulant and circulant matrices have important applications in various networks engineering
We discuss the invertibility of skew circulant type matrices with any continuous Fibonacci numbers and present the determinant and the inverse matrices by constructing the transformation matrices
On the basis of existing application situation [1,2,3,4,5,6,7,8,9,10,11], we will exploit application of network engineering based on skew circulant matrix

Summary

Introduction

Skew circulant and circulant matrices have important applications in various networks engineering. Some authors gave the explicit determinants and inverses of circulant and skew circulant matrices involving some famous numbers. Yao and Jiang [21] considered the determinants, inverses, norm, and spread of skew circulant type matrices involving any continuous Lucas numbers. Gao et al [23] gave explicit determinants and inverses of skew circulant and skew left circulant matrices with Fibonacci and Lucas numbers. The determinants, inverses, norm, and spread of skew circulant type matrices involving any continuous Lucas numbers are considered in [21]. The purpose of this paper is to obtain the explicit determinants, explicit inverses, norm, and spread of skew circulant type matrices involving any continuous Fibonacci numbers.

Determinant and Inverse of Skew Circulant Matrix with the Fibonacci Numbers

Norm and Spread of Skew Circulant Matrix with the Fibonacci Numbers

Norm and Spread of Skew Left Circulant Matrix with the Fibonacci Numbers

Conclusion