Jump to ContentJump to Main Navigation
Matrix Completions, Moments, and Sums of Hermitian Squares$
Users without a subscription are not able to see the full content.

Mihály Bakonyi and Hugo J. Woerdeman

Print publication date: 2011

Print ISBN-13: 9780691128894

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691128894.001.0001

Show Summary Details
Page of

PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2017. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in HSO for personal use (for details see http://www.universitypressscholarship.com/page/privacy-policy).date: 13 December 2017

Hermitian and related completion problems

Hermitian and related completion problems

Chapter:
(p.361) Chapter Five Hermitian and related completion problems
Source:
Matrix Completions, Moments, and Sums of Hermitian Squares
Author(s):

Mihály Bakonyi

Hugo J. Woerdeman

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691128894.003.0005

This chapter considers various completion problems that are in one way or another closely related to positive semidefinite or contractive completion problems. For instance, as a variation on requiring that all eigenvalues of the completion are positive/nonnegative, one can consider the question how many eigenvalues of a Hermitian completion have to be positive/nonnegative. In the solution to the latter problem ranks of off-diagonal parts will play a role, which is why minimal rank completions are also discussed. Related is a question on real measures on the real line. As a variation of the contractive completion problem, the chapter considers the question how many singular values of a completion have to be smaller (or larger) than one. It also looks at completions in classes of normal matrices and distance matrices. As applications it turns to questions regarding Hermitian matrix expressions, a minimal representation problem for discrete systems, and the separability problem that appears in quantum information. Exercises and notes are provided at the end of the chapter.

Keywords:   completion problems, positive semidefinite completion, contractive completion, minimal rank completions, Hermitian matrix expressions, separability problem

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.