Revista de teoría y aplicaciones de la mentira generalizada

A Horn type spectral problem 1

Abstract

Stanislav POPOVYCH

The famous Horn’s problem is about the possible eigenvalue list of a sum of two Hermitian matrices with prescribed eigenvalue lists. The Spectral Problem is to describe possible spectra for an irreducible finite family of Hermitian operators with the sum being a scalar operator. In case when spectra consist of finite number of points the complexity of the problem depends on properties of some rooted tree. We will consider the cases for which the explicit answer on the Spectral Problem can be obtained.