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Radial eigenvectors of the Laplacian of the nonbinary hypercube

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Title Radial eigenvectors of the Laplacian of the nonbinary hypercube
 
Creator SRINIVASAN, MK
 
Subject Laplacian eigenvalues
Nonbinary hypercube
Radial eigenvectors
 
Description Let q be a positive integer >= 2. Define a (n + 1) x (n + 1) real, symmetric, tridiagonal matrix M, with rows and columns indexed by {0, 1, ... , n), and with entries given by: M(i, j) = {-root(q - 1)(n - j + 1) if i = j - 1, j + (1 - n)(n - j) if i = j, -root(q - 1)(j + 1)(n - j) if i = j + 1, 0 if vertical bar i - j vertical bar >= 2. The (n + 1)-dimensional space of radial vectors for the nonbinary hypercube C-q(n) is invariant under the Laplacian and M arises as the matrix of the Laplacian with respect to a suitable orthonormal basis of radial vectors. We show that the eigenvalues of M are 0, q, 2q, ... , nq by explicitly writing down the eigenvectors. (C) 2012 Elsevier Inc. All rights reserved.
 
Publisher ELSEVIER SCIENCE INC
 
Date 2014-10-14T17:34:28Z
2014-10-14T17:34:28Z
2013
 
Type Article
 
Identifier LINEAR ALGEBRA AND ITS APPLICATIONS, 438(5)2557-2560
http://dx.doi.org/10.1016/j.laa.2012.10.019
http://dspace.library.iitb.ac.in/jspui/handle/100/14580
 
Language en