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Journal of Applied Mathematics
Volume 2014, Article ID 239693, 10 pages
http://dx.doi.org/10.1155/2014/239693
Research Article

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

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

Received 6 January 2014; Accepted 17 February 2014; Published 17 April 2014

Academic Editor: Feng Gao

Copyright © 2014 Jin-jiang Yao and Zhao-lin Jiang. 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

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.