Positivity of partitioned Hermitian matrices with unitarily invariant norms

Positivity of partitioned Hermitian matrices with unitarily invariant norms We give a short proof of a recent result of Drury on the positivity of a $$3\times 3$$ 3 × 3 matrix of the form $$(\Vert R_i^*R_j\Vert _{\mathop {\mathrm{tr}}\,})_{1 \le i, j \le 3}$$ ( ‖ R i ∗ R j ‖ tr ) 1 ≤ i , j ≤ 3 for any rectangular complex (or real) matrices $$R_1, R_2, R_3$$ R 1 , R 2 , R 3 so that the multiplication $$R_i^*R_j$$ R i ∗ R j is compatible for all $$i, j,$$ i , j , where $$\Vert \cdot \Vert _{\mathop {\mathrm{tr}}\,}$$ ‖ · ‖ tr denotes the trace norm. We then give a complete analysis of the problem when the trace norm is replaced by other unitarily invariant norms. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Positivity of partitioned Hermitian matrices with unitarily invariant norms

Loading next page...
 
/lp/springer_journal/positivity-of-partitioned-hermitian-matrices-with-unitarily-invariant-B0lHozElOK
Publisher
Springer Journals
Copyright
Copyright © 2014 by Springer Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-014-0306-4
Publisher site
See Article on Publisher Site

Abstract

We give a short proof of a recent result of Drury on the positivity of a $$3\times 3$$ 3 × 3 matrix of the form $$(\Vert R_i^*R_j\Vert _{\mathop {\mathrm{tr}}\,})_{1 \le i, j \le 3}$$ ( ‖ R i ∗ R j ‖ tr ) 1 ≤ i , j ≤ 3 for any rectangular complex (or real) matrices $$R_1, R_2, R_3$$ R 1 , R 2 , R 3 so that the multiplication $$R_i^*R_j$$ R i ∗ R j is compatible for all $$i, j,$$ i , j , where $$\Vert \cdot \Vert _{\mathop {\mathrm{tr}}\,}$$ ‖ · ‖ tr denotes the trace norm. We then give a complete analysis of the problem when the trace norm is replaced by other unitarily invariant norms.

Journal

PositivitySpringer Journals

Published: Sep 14, 2014

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off