An Application of Caratheodory's Theorem
to the Spectral Set Problem for Convex Matrix Sets
Vladimir Monov
Institute of Information Technologies, 1113 Sofia
Abstract: Let K be a compact and convex set of nxn real matrices. The paper presents an application of the well known Caratheodory's theorem to the problem of characterizing the spectral set of K. In particular, using this theorem, it is shown that the entire spectral set can be obtained from the spectra of convex polytopes in K having dimension no greater than 2n. In general, this result enables us to study the spectral properties of K by examining lower-dimensional convex subsets of K.