Mathematics Faculty Articles

Title

Positivity of partitioned Hermitian matrices with unitarily invariant norms

Document Type

Article

Publication Date

9-24-2015

Publication Title

Positivity

Keywords

Polar decomposition, Positive semi-definite matrix, Trace norm, Unitarily invariant norm

ISSN

13851292

Volume

19

Issue/No.

3

First Page

439

Last Page

444

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

Share

COinS