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Abstract and Applied Analysis
Volume 2014, Article ID 931451, 14 pages
Research Article

The Invertibility, Explicit Determinants, and Inverses of Circulant and Left Circulant and -Circulant Matrices Involving Any Continuous Fibonacci and Lucas Numbers

Department of Mathematics, Linyi University, Linyi, Shandong 276000, China

Received 28 February 2014; Accepted 7 July 2014; Published 20 July 2014

Academic Editor: Chuangxia Huang

Copyright © 2014 Zhaolin Jiang and Dan Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Circulant matrices play an important role in solving delay differential equations. In this paper, circulant type matrices including the circulant and left circulant and -circulant matrices with any continuous Fibonacci and Lucas numbers are considered. Firstly, the invertibility of the circulant matrix is discussed and the explicit determinant and the inverse matrices by constructing the transformation matrices are presented. Furthermore, the invertibility of the left circulant and -circulant matrices is also studied. We obtain the explicit determinants and the inverse matrices of the left circulant and -circulant matrices by utilizing the relationship between left circulant, -circulant matrices and circulant matrix, respectively.