Skip to main content Accessibility help
×
Home
Hostname: page-component-768ffcd9cc-9th95 Total loading time: 0.535 Render date: 2022-12-03T02:05:01.817Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true

TRACE INEQUALITIES FOR MATRICES

Published online by Cambridge University Press:  02 August 2012

KHALID SHEBRAWI*
Affiliation:
Department of Mathematics, Faculty of Science, Al-Balqa’ Applied University, Salt, Jordan Department of Mathematics, Faculty of Science, Qassim University, Qassim, Saudi Arabia (email: shebrawi@gmail.com)
HUSSIEN ALBADAWI
Affiliation:
Preparatory Year Deanship, King Faisal University, Ahsaa, Saudi Arabia (email: halbadawi@kfu.edu.sa)
*
For correspondence; e-mail: shebrawi@gmail.com
Rights & Permissions[Opens in a new window]

Abstract

HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Trace inequalities for sums and products of matrices are presented. Relations between the given inequalities and earlier results are discussed. Among other inequalities, it is shown that if A and B are positive semidefinite matrices then for any positive integer k.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

References

[1]Ando, T., ‘Matrix Young inequalities’, Oper. Theory Adv. Appl. 75 (1995), 3338.Google Scholar
[2]Bhatia, R., Positive Definite Matrices (Princeton University Press, Princeton, NJ, 2007).Google Scholar
[3]Chen, L. and Wong, C., ‘Inequalities for singular values and traces’, Linear Algebra Appl. 171 (1992), 109120.CrossRefGoogle Scholar
[4]Coope, I. D., ‘On matrix trace inequalities and related topics for products of Hermitian matrices’, J. Math. Anal. Appl. 188 (1994), 9991001.CrossRefGoogle Scholar
[5]Fujii, J., ‘A trace inequality arising from quantum information theory’, Linear Algebra Appl. 400 (2005), 141146.CrossRefGoogle Scholar
[6]Manjegani, S., ‘Hölder and Young inequalities for the trace of operators’, Positivity 11 (2007), 239250.CrossRefGoogle Scholar
[7]Marshall, A. W. and Olkin, I., Inequalities: Theory of Majorization and its Applications (Academic Press, San Diego, CA, 1979).Google Scholar
[8]Shebrawi, K. and Albadawi, H., ‘Operator norm inequalities of Minkowski type’, J. Inequal. Pure Appl. Math. 9(1) (2008), 110, article 26.Google Scholar
[9]Shebrawi, K. and Albadawi, H., ‘Numerical radius and operator norm inequalities’, J. Inequal. Appl. 2009 article 492154.Google Scholar
[10]Simon, B., Trace Ideals and Their Applications (Cambridge University Press, Cambridge, 1979).Google Scholar
[11]Yang, X., ‘Some trace inequalities for operators’, J. Aust. Math. Soc. A 58 (1995), 281286.CrossRefGoogle Scholar
[12]Yang, X., ‘A matrix trace inequality’, J. Math. Anal. Appl. 250 (2000), 372374.CrossRefGoogle Scholar
[13]Yang, X. M., Yang, X. Q. and Teo, K. L., ‘A matrix trace inequality’, J. Math. Anal. Appl. 263 (2001), 327331.CrossRefGoogle Scholar
[14]Zhan, X., Matrix Inequalities (Springer, Berlin, 2002).CrossRefGoogle Scholar
You have Access
12
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

TRACE INEQUALITIES FOR MATRICES
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

TRACE INEQUALITIES FOR MATRICES
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

TRACE INEQUALITIES FOR MATRICES
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *