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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 515082, 6 pages
http://dx.doi.org/10.1155/2014/515082
Research Article

A Test Matrix for an Inverse Eigenvalue Problem

1Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, ON, Canada N2L 3G1
2Department of Mathematics, Bishop’s University, Sherbrooke, QC, Canada J1M 2H2

Received 21 February 2014; Accepted 30 April 2014; Published 26 May 2014

Academic Editor: K. C. Sivakumar

Copyright © 2014 G. M. L. Gladwell 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

We present a real symmetric tridiagonal matrix of order whose eigenvalues are which also satisfies the additional condition that its leading principle submatrix has a uniformly interlaced spectrum, . The matrix entries are explicit functions of the size , and so the matrix can be used as a test matrix for eigenproblems, both forward and inverse. An explicit solution of a spring-mass inverse problem incorporating the test matrix is provided.