On a problem of O. Taussky

Bernard Werner Levinger and Richard Steven Varga

Vol. 19 (1966), No. 3, 473–487

DOI: 10.2140/pjm.1966.19.473

Abstract

Recently, O. Taussky raised the following question. Given a nonnegative n×n matrix A = (a_i,j), let Ω_A be the set of all n × n complex matrices defined by

Then, defining the spectrum S(M) of an arbitrary set M of n × n matrices B as

what can be said in particular about S(Ω_A)? It is not difficult to see that S(Ω_A) consists of possibly one disk and a series of annular regions concentric about the origin, but our main result is a precise characterization of S(Ω_A) in terms of the minimal Gerschgorin sets for A.

Mathematical Subject Classification

Primary: 15.25

Milestones

Received: 29 October 1964

Published: 1 December 1966