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Abstract and Applied Analysis
Volume 2014, Article ID 238953, 9 pages
http://dx.doi.org/10.1155/2014/238953
Research Article

Invertibility and Explicit Inverses of Circulant-Type Matrices with -Fibonacci and -Lucas Numbers

Department of Mathematics, Linyi University, Linyi, Shandong 276005, China

Received 27 March 2014; Accepted 17 April 2014; Published 20 May 2014

Academic Editor: Juntao Sun

Copyright © 2014 Zhaolin Jiang et al. 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.

Abstract

Circulant matrices have important applications in solving ordinary differential equations. In this paper, we consider circulant-type matrices with the -Fibonacci and -Lucas numbers. We discuss the invertibility of these circulant matrices and present the explicit determinant and inverse matrix by constructing the transformation matrices, which generalizes the results in Shen et al. (2011).