Article
Positivity of partitioned Hermitian matrices with unitarily invariant norms
Positivity
Document Type
Article
Publication Date
9-24-2015
Keywords
- Polar decomposition,
- Positive semi-definite matrix,
- Trace norm,
- Unitarily invariant norm
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.
DOI
10.1007/s11117-014-0306-4
Citation Information
Chi Kwong Li and Fuzhen Zhang. "Positivity of partitioned Hermitian matrices with unitarily invariant norms" Positivity Vol. 19 Iss. 3 (2015) p. 439 - 444 ISSN: 13851292 Available at: http://works.bepress.com/fuzhen-zhang/181/