Upper bounds for the spectral radius of the n×n Hilbert matrix

Peter Otte

Vol. 219 (2005), No. 2, 323–331

DOI: 10.2140/pjm.2005.219.323

Abstract

We derive upper bounds for the spectral radius of the n × n Hilbert matrix. The key idea is to write the Hilbert matrix as integral operator with positive kernel function and then to use a Wielandt-type min-max principle for the spectral radius. Choosing special trial functions yields a new bound that improves the best bound known heretofore.

Keywords

Hilbert matrix, Hilbert inequality, spectral radius, Wielandt min-max principle, integral operator

Mathematical Subject Classification 2000

Primary: 15A42, 15A60, 47G10

Milestones

Received: 20 October 2003

Revised: 19 March 2004

Published: 1 April 2005