摘要：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.
