Cited by 343Mathematical Inequalities and ApplicationsMatrix Theory and AlgorithmsAdvanced Combinatorial Mathematics

A trace inequality of John von Neumann

Mirsky, L.·1975·Monatshefte für Mathematik

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Crossref · 10.1007/bf01647331

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6 of 6 references verified0 citation errors · 0 not checkable

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  • The von Neumann trace inequality holds for any complex n by n matrices with descending singular values.

    “Inequality (7) holds for any complex n  n matrices A 1 and A 2 with descending singular values, 1;1 ! . . .! 1;n and 2;1 ! . . .! 2;n .”

    From Quantum Speed Limit for Non-Markovian Dynamics (2013) · cites this paper as [22]

  • The von Neumann trace inequality bounds the absolute trace of a product of matrices by the sum of products of their singular values.

    “To proceed, we introduce the von Neumann trace inequality for operators which reads [141], |tr {A 1 A 2 }| n i=1 σ 1,i σ 2,i .(79)”

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Authors
Mirsky, L.
Affiliations
University of Sheffield (GB)
Corresponding author
Mirsky, L.
Venue
Monatshefte für Mathematik
Published
1975-12
Volume
79
Issue
4
Pages
303-306
ISSN
  • 0026-9255 (ISSN-L)
  • 1436-5081
OpenAlex
W2056532343
Cited by
343
References
6
Citations by year
2026: 21 · 2025: 19 · 2024: 32 · 2023: 27 · 2022: 29 · 2021: 33 · 2020: 25 · 2019: 24 · 2018: 21 · 2017: 24 · 2016: 23 · 2015: 13 · 2014: 10 · 2013: 18 · 2012: 5
FWCI
0.60
Type
journal article
Language
en
Open access
closed
Locations
Monatshefte für Mathematik (publishedVersion)
Topics
  • Physical Sciences › Mathematics › Applied Mathematics › Mathematical Inequalities and Applications
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
  • Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Advanced Combinatorial Mathematics
Keywords
singular values, matrix trace, complex matrices, matrix inequalities, singular value decomposition

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