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Mathematical Problems in Engineering
Volume 2014, Article ID 518913, 7 pages
Research Article

The Explicit Identities for Spectral Norms of Circulant-Type Matrices Involving Binomial Coefficients and Harmonic Numbers

Department of Mathematics, Linyi University, Shandong 276005, China

Received 17 October 2013; Accepted 23 December 2013; Published 12 January 2014

Academic Editor: Masoud Hajarian

Copyright © 2014 Jianwei Zhou 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.


The explicit formulae of spectral norms for circulant-type matrices are investigated; the matrices are circulant matrix, skew-circulant matrix, and -circulant matrix, respectively. The entries are products of binomial coefficients with harmonic numbers. Explicit identities for these spectral norms are obtained. Employing these approaches, some numerical tests are listed to verify the results.