Advanced search

Browse by subject

Browse by provider

Browse by language

Content Details
Normal View
CIP View

A note on the non-commutative arithmetic...

Zhang, Teng...

Free

Share this content

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

Review the full bibliography data and make any necessary corrections before using. Always consult your library resources for the exact formatting and punctuation guidelines.

AMA 11th EditionReferences

Zhang, Teng. A note on the non-commutative arithmetic-geometric mean inequality. Australian National University. September 06, 2023. Accessed November 11, 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 11 November 2024).

Harvard AustraliaReferences

Zhang, Teng, 2023, A note on the non-commutative arithmetic-geometric mean inequality, Australian National University, viewed 11 November 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.

Share this eBook