On Symmetric Solution Sets

Given an n x n interval matrix [A] and an interval vector [b] with n components we present an overview on existing results on the solution set S_sym of linear systems of equations Ax = b with symmetric matrices A E [A] and vectors b E [b]. Similarly we consider the set E_sym of eigenpairs associated with the symmetric matrices A E [Al. We report on characterizations of _Ssym by means of inequalities, by means of intersection of sets, and by an approach which is generalizable to more general dependencies of the entries. We also recall two methods for enclosing S_sym by means of interval vectors, and we mention a characterization of Es _y m.