On Nonsingularity of Saddle Point Matrices with Vectors of Ones
Tadeusz Ostrowski · 2008
This paper describes and analyzes nonsingularity conditions of saddle point matrices with two vector blocks of ones. These kind of matrices occur in standard quadratic pro-gram (when the left-up block is a symmetric matrix) and in game theory (when the left-up block is any square matrix) or in special linear systems called equilibrium systems. Necessary and sufficient conditions for the nonsingularity are investigated. We review some known conditions in the literature as well.