Radial eigenvectors of the Laplacian of the nonbinary hypercube
DSpace at IIT Bombay
View Archive InfoField | Value | |
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
|
|