International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 8, Pages 563-566

Cauchy's interlace theorem and lower bounds for the spectral radius

A. McD. Mercer1 and Peter R. Mercer2

1Department of Mathematics and Statistics, University of Guelph, Ontario, N1G-2W1, Canada
2Department of Mathematics, SUNY College at Buffalo, 14222, NY, USA

Received 31 December 1998

Copyright © 2000 A. McD. Mercer and Peter R. Mercer. 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.


We present a short and simple proof of the well-known Cauchy interlace theorem. We use the theorem to improve some lower bound estimates for the spectral radius of a real symmetric matrix.