Real Zero Polynomials and A. Horn's Problem

TL;DR

This paper explores the connection between Horn's problem for self-adjoint matrices and real zero polynomials, proposing an algorithm to construct matrix pairs with prescribed spectra based on polynomial interpolation and moment problems.

Contribution

It establishes a novel link between Horn's problem and real zero polynomial interpolation, providing a new algorithm for matrix construction.

Findings

Connection between Horn's problem and real zero polynomials

Development of an algorithm for matrix pair construction

Insight into spectral prescription via polynomial interpolation

Abstract

A. Horn's problem concerns find two self adjoint matrices A, B, so that A, B, and A+B have prescribed spectrum. In this paper, we show how it connects to an interpolation problem for two variable real zero polynomials and a tracial moment problem. In addition, we outline an algorithm to construct a pair (A,B).