A Normal Variation of the Horn Problem: The Rank 1 Case

Authors

Lei Cao, Drexel UniversityFollow
Hugo J. Woerdeman, Drexel University

Document Type

Article

Publication Date

10-1-2014

Publication Title

Annals of Functional Analysis

Keywords

The problem of A. Horn, Normal matrices, Upper Hessenberg

ISSN

2008-8752

Volume

5

Issue/No.

2

First Page

138

Last Page

146

Abstract

Given three n-tuples {λ_i}ⁿ_i=1, {μ_i}ⁿ_i=1, {v_i}ⁿ_i=1 of complex numbers, we introduce the problem of when there exists a pair of normal matrices A and B such that σ(A) = {λ_i}ⁿ_i=1, σ(B) = {μ_i}ⁿ_i=1, and σ(A+B) = {v_i}ⁿ_i=1, where σ(.) denote that spectrum. In the case when λ_k = 0, k = 2,...,n, we provide necessary and sufficient conditions for the existence of A and B. In addition, we show that the solution pair (A,B) is unique up to unitary similarity. The necessary and sufficient conditions reduce to the classical A. Horn inequalities when n-tuples are real.

Comments

©2014 Duke University Press

Additional Comments

NSF grant #: DMS-0901628

NSUWorks Citation

Cao, Lei and Woerdeman, Hugo J., "A Normal Variation of the Horn Problem: The Rank 1 Case" (2014). Mathematics Faculty Articles. 267.
https://nsuworks.nova.edu/math_facarticles/267

ORCID ID

0000-0001-7613-7191

ResearcherID

G-7341-2019