An Oettli--Prager-Like Theorem for the Symmetric Solution Set and for Related Solution Sets

Abstract

We recall three equivalent characterizations of the solution set of linear systems of equations with perturbed input data, and reformulate and modify slightly Hladik's Oettli--Prager-like theorem for describing the corresponding symmetric solution set. Based on this modification we are able to derive and prove this theorem in a new, elementary way and to reduce the number of inequalities essentially. In the same way we reformulate and reprove Hladik's result on the skew-symmetric solution set and derive a new characterization for the persymmetric and the perskew-symmetric solution set.