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• W2149303655 abstract "Recently, Chau [Quant. Inform. & Comp. 11, 721 (2011)] showed that one can define certain metrics and pseudo-metrics on U(n), the group of all $ntimes n$ 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 ${mathbb R}^n$ 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]." @default.
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• W2149303655 date "2012-02-16" @default.
• W2149303655 modified "2023-10-01" @default.
• W2149303655 title "Induced metric and matrix inequalities on unitary matrices" @default.
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• W2149303655 doi "https://doi.org/10.1088/1751-8113/45/9/095201" @default.
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