Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/25086
Title: Induced metric and matrix inequalities on unitary matrices
Authors: Chau, HF
Li, CK
Poon, YT
Sze, NS 
Issue Date: 2012
Publisher: IOP Publishing Ltd
Source: Journal of physics a : mathematical and theoretical, 2012, v. 45, no. 9, 95201 How to cite?
Journal: Journal of Physics A: Mathematical and Theoretical 
Abstract: Recently, Chau (2011 Quantum Inform. Comput. 11 721) showed that one can define certain metrics and pseudo-metrics on U(n), the group of all n × n unitary matrices, based on the arguments of the eigenvalues of the unitary matrices. More importantly, these metrics and pseudo-metrics have quantum information theoretical meanings. So it is instructive to study this kind of metrics and pseudo-metrics on U(n). Here we show that any symmetric norm on ℝ n induces a metric on U(n). Furthermore, using the same technique, we prove an inequality concerning the eigenvalues of a product of two unitary matrices which generalizes a few inequalities obtained earlier by Chau (arXiv:1006.3614v1).
URI: http://hdl.handle.net/10397/25086
ISSN: 1751-8113
DOI: 10.1088/1751-8113/45/9/095201
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