International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 8, Pages 563-566
doi:10.1155/S016117120000257X
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
Abstract
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.