Abstract
We give a short proof of a recent result of Drury on the positivity of a (Formula presented.) matrix of the form (Formula presented.) for any rectangular complex (or real) matrices (Formula presented.) so that the multiplication (Formula presented.) is compatible for all (Formula presented.) where (Formula presented.) denotes the trace norm. We then give a complete analysis of the problem when the trace norm is replaced by other unitarily invariant norms.
| Original language | American English |
|---|---|
| Pages (from-to) | 439-444 |
| Number of pages | 6 |
| Journal | Positivity |
| Volume | 19 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 24 2015 |
Bibliographical note
Publisher Copyright:© 2014, Springer Basel.
Funding
| Funders |
|---|
| National Science Foundation |
ASJC Scopus Subject Areas
- Analysis
- Theoretical Computer Science
- General Mathematics
Keywords
- Unitarily invariant norm
- Polar decomposition
- Positive semi-definite matrix
- Trace norm
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