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Mathematics Faculty Articles
A Normal Variation of the Horn Problem: The Rank 1 Case
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 {λi}ni=1, {μi}ni=1, {vi}ni=1 of complex numbers, we introduce the problem of when there exists a pair of normal matrices A and B such that σ(A) = {λi}ni=1, σ(B) = {μi}ni=1, and σ(A+B) = {vi}ni=1, where σ(.) denote that spectrum. In the case when λk = 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.
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
Comments
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