On the eigenvalues of interval matrices

In this paper we will examine how the spectrum (of eigenvalues) of an interval matrix family M depends on the spectrum of its extreme sets. We present three results: 1) We show that the roots of pairwise convex combinations of the characteristic polynomials of the vertices of M provide a bound for the spectrum of M. 2) We state conditions on M which guarantee that the spectrum of M can be determined from the spectrum of its relative boundary. 3) For the special case of M having a real spectrum, we show that this spectrum is completely determined by the eigenvalues of its vertices.