Description of Symmetric and Skew–Symmetric Solution Set
Milan Hladík · SIAM Journal on Matrix Analysis and Applications · 2008
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 Oettli–Prager Theorem. But if we are restricted only on symmetric/skew–symmetric matrices $A\in\mathbf{A}$, the problem is much more complicated. So far, the symmetric/skew–symmetric solution set description could be obtained only by a lengthy Fourier–Motzkin elimination applied on each orthant. We present an explicit necessary and sufficient characterization of the symmetric and skew–symmetric solution set by means of nonlinear inequalities. The number of the inequalities is, however, still exponential w.r.t. the problem dimension.