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Abstract and Applied Analysis
Volume 2014, Article ID 381829, 9 pages
http://dx.doi.org/10.1155/2014/381829
Research Article

Determinants, Norms, and the Spread of Circulant Matrices with Tribonacci and Generalized Lucas Numbers

1Department of Mathematics, Linyi University, Linyi, Shandong 276000, China
2Department of Mathematics, Shandong Normal University, Ji’nan, Shandong 250014, China

Received 28 March 2014; Accepted 26 April 2014; Published 11 May 2014

Academic Editor: Tongxing Li

Copyright © 2014 Juan Li 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 play an important role in solving ordinary and partial differential equations. In this paper, by using the inverse factorization of polynomial of degree n, the explicit determinants of circulant and left circulant matrix involving Tribonacci numbers or generalized Lucas numbers are expressed in terms of Tribonacci numbers and generalized Lucas numbers only. Furthermore, four kinds of norms and bounds for the spread of these matrices are given, respectively.