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A note on the non-commutative arithmetic...

Zhang, Teng...

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A note on the non-commutative arithmetic-geometric mean inequality by Zhang, Teng ( Author )

Content Provider	Lemonjar Open Access
Publisher	Australian National University
Publication Date	06-09-2023
Summary	This note proves the following inequality: if $n=3k$ for some positive integer $k$, then for any $n$ positive definite matrices $A_1,A_2,\cdots,A_n$, \begin{equation} \frac{1}{n^3}\Big\\|\sum_{j_1,j_2,j_3=1}^{n}A_{j_1}A_{j_2}A_{j_3}\Big\\| \geq \frac{(n-3)!}{n!} \Big\\|\sum_{\substack{j_1,j_2,j_3=1,\\\text{$j_1$, $j_2$, $j_3$ all distinct}}}^{n}A_{j_1}A_{j_2}A_{j_3}\Big\\|, \end{equation} where $\\|\cdot\\|$ represents the operator norm. This inequality is a special case of a recent conjecture by Recht and R\'e.
ISBN	-
Item Type	Article
File Type	pdf
File Size	29.34 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	http://arxiv.org/abs/1411.5058

Citation

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AMA 11th EditionReferences

Zhang, Teng. A note on the non-commutative arithmetic-geometric mean inequality. Australian National University. September 06, 2023. Accessed September 20, 2024. https://online.provdatabase.com/cite/23889

APA 7th EditionReferences

Zhang, Teng. (2023). A note on the non-commutative arithmetic-geometric mean inequality. Australian National University. https://online.provdatabase.com/cite/23889

Chicago 17th EditionReferences

Zhang, Teng. A note on the non-commutative arithmetic-geometric mean inequality. Australian National University. 2023. https://online.provdatabase.com/cite/23889

HarvardReferences

Zhang, Teng. (2023). A note on the non-commutative arithmetic-geometric mean inequality. [Online]. Australian National University. Available from: https://online.provdatabase.com/cite/23889. (Accessed 20 September 2024).

Harvard AustraliaReferences

Zhang, Teng, 2023, A note on the non-commutative arithmetic-geometric mean inequality, Australian National University, viewed 20 September 2024, <https://online.provdatabase.com/cite/23889>

MLA 9th EditionWorks Cited

Zhang, Teng. A note on the non-commutative arithmetic-geometric mean inequality. Australian National University, 2023. PROV Database, https://online.provdatabase.com/cite/23889.

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