Skip to main content

Probability Inequalities for Matrices

  • 2800 Accesses

Part of the Lecture Notes in Mathematics book series (LNMECOLE,volume 2159)

Abstract

A selection of probability inequalities from the literature for sums of mean zero matrices is presented. The chapter starts out with recalling Hoeffding’s inequality and Bernstein’s inequality. Then symmetric matrices and rectangular matrices are considered (the latter mostly in Sects. 9.3 and 9.4). The paper Tropp (2012) serves as main reference and in Sect. 9.4 result from Lounici (2011). See also Tropp (2015) for further results.

Keywords

  • Probability Inequalities
  • Hoeffding
  • Rectangular Matrices
  • Symmetric Matrices
  • Mean Zero

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

van de Geer, S. (2016). Probability Inequalities for Matrices. In: Estimation and Testing Under Sparsity. Lecture Notes in Mathematics(), vol 2159. Springer, Cham. https://doi.org/10.1007/978-3-319-32774-7_9

Download citation