Gersgorin variations I: on a theme of Pupkov and Solovʹev Original Research Article

We unify and extend various “additive” sufficient conditions of Pupkov and of Solovʹev 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.