Description of symmetric and skew-symmetric solution set

Abstract

We consider a linear system Ax=b, where A is varying inside a given interval matrix [A], and b is varying inside a given interval vector [b]. The solution set of such a system is described by the well-known OettliPrager Theorem.

But if we are restricted only on symmetric/skewsymmetric matrices in [A], the problem is much more complicated. So far, the symmetric/skewsymmetric solution set description could be obtained only by a lengthy FourierMotzkin elimination applied on each orthant.

We present an explicit necessary and sufficient characterization of the symmetric and skewsymmetric solution set by means of nonlinear inequalities. The number of the inequalities is, however, still exponential w.r.t. the problem dimension.

Keywords

• Description
• symmetric
• skew-symmetric
• solution
• set