Abstract
The principal aim of this note is to establish an effectively self-contained proof of J. von Neumann's inequality\(\left| {tr\left( {AB} \right)} \right| \leqslant \sum\limits_{r = 1}^n {\varrho _r \sigma _r } \), whereA, B are any complexn×n matrices with singular values ϱ1⩾...⩾ϱ n , σ1⩾...⩾σ n respectively.
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Mirsky, L. A trace inequality of John von Neumann. Monatshefte für Mathematik 79, 303–306 (1975). https://doi.org/10.1007/BF01647331
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DOI: https://doi.org/10.1007/BF01647331