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Journal article
A NORMAL VARIATION OF THE HORN PROBLEM: THE RANK 1 CASE
Annals of functional analysis, v 5(2)
01 Jan 2014
Abstract
Given three n-tuples {lambda(i)}(i)(n)(=1), {mu(i)}(i)(n)(=1), {nu(i)}(i)(n)(=1) of complex numbers, we introduce the problem of when there exists a pair of normal matrices A and B such that sigma(A) = {lambda(i)}(i)(n)(=1), sigma(B) = {mu(i)}(i)(n)(=1), and sigma(A + B) = {nu(i)}(i)(n)(=1), where sigma(center dot) denote the spectrum. In the case when lambda(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 the n-tuples are real.
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Details
- Title
- A NORMAL VARIATION OF THE HORN PROBLEM: THE RANK 1 CASE
- Creators
- Lei Cao - Drexel Univ, Dept Math, Philadelphia, PA 19104 USAHugo J. Woerdeman - Drexel University
- Publication Details
- Annals of functional analysis, v 5(2)
- Publisher
- Tusi Mathematical Research Group
- Number of pages
- 9
- Grant note
- DMS-0901628 / NSF; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000346128900011
- Scopus ID
- 2-s2.0-84932145087
- Other Identifier
- 991019169326104721
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- Web of Science research areas
- Mathematics
- Mathematics, Applied