Table of Contents
International Journal of Computational Mathematics
Volume 2014 (2014), Article ID 795175, 6 pages
http://dx.doi.org/10.1155/2014/795175
Research Article

On the Spectrum and Spectral Norms of -Circulant Matrices with Generalized -Horadam Numbers Entries

College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Received 17 May 2014; Accepted 25 August 2014; Published 31 August 2014

Academic Editor: Chengpeng Bi

Copyright © 2014 Lele Liu. 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

This work is concerned with the spectrum and spectral norms of -circulant matrices with generalized -Horadam numbers entries. By using Abel transformation and some identities we obtain an explicit formula for the eigenvalues of them. In addition, a sufficient condition for an -circulant matrix to be normal is presented. Based on the results we obtain the precise value for spectral norms of normal -circulant matrix with generalized -Horadam numbers, which generalize and improve the known results.