Year: 1995
Type: article
Abstract: A fundamental result of von Neumann’s identifies unitarily invariant matrix norms as symmetric gauge functions of the singular values. Identifying the subdifferential of such a norm is important in matrix approximation algorithms, and in studying the geometry of the corresponding unit ball. We show how to reduce many convex-analytic questions of this kind to questions about the underlying gauge function, via an elegant Fenchel conjugacy formula. This approach also allows such results to be extended to more general unitarily invariant matrix functions.
Source: Journal of convex analysis
DOI: 10.68381/jca02012
Author: A.S. Lewis
Institution: University of Waterloo
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2149934276