Monatshefte für Mathematik

, Volume 79, Issue 4, pp 303–306

A trace inequality of John von Neumann

  • L. Mirsky

DOI: 10.1007/BF01647331

Cite this article as:
Mirsky, L. Monatshefte für Mathematik (1975) 79: 303. doi:10.1007/BF01647331


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⩾...⩾ϱn, σ1⩾...⩾σn respectively.

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • L. Mirsky
    • 1
  1. 1.Department of Pure MathematicsUniversity of SheffieldSheffieldEngland

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