Gersgorin variations I: On a theme of Pupkov and Solov'ev

We unify and extend various "additive" sufficient conditions of Pupkov and of Solov'ev for the nonsingularity of a complex matrix. This paper is intended to be the first in a sequcnce of "variations" on theorems of the Gersgorin genre. The whole sequence is dedicated to the memory of Olga Taussky-Todd, whose lovely paper [O. Taussky, Amer. Math. Monthly 56 (1949) 672-676,] inspired an interest in matrix theory for a generation of mathematicians. © 2000 Elsevier Science Inc.