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
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.