Abstract
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.
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