A trace inequality of John von Neumann
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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)”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [141]
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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
- Licence
- www.springer.com/tdm (tdm)
- 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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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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