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arXiv · 1006.3978

Elementary Proofs Of Two Theorems Involving Arguments Of Eigenvalues Of A Product Of Two Unitary Matrices

H. F. Chau·Y. T. Lam
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Abstract

We give elementary proofs of two theorems concerning bounds on the maximum argument of the eigenvalues of a product of two unitary matrices --- one by Childs \emph{et al.} [J. Mod. Phys., \textbf{47}, 155 (2000)] and the other one by Chau [arXiv:1006.3614]. Our proofs have the advantages that the necessary and sufficient conditions for equalities are apparent and that they can be readily generalized to the case of infinite-dimensional unitary operators.

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BibTeXRIS

H. F. Chau, Y. T. Lam. 2010-06-21. Elementary Proofs Of Two Theorems Involving Arguments Of Eigenvalues Of A Product Of Two Unitary Matrices. https://arxiv.org/abs/1006.3978

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