International Journal of Computer Engineering Research
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Article Number - 7C6247F8655


Vol.3(3), pp. 50 - 54 , May 2012
DOI: 10.5897/IJCER12.013
ISSN: 2141-6494



Full Length Research Paper

New Holder-type inequalities for the Tracy-Singh and Khatri-Rao products of positive matrices


Zeyad AL-Zhour




Email: zeyad1968@yahoo.com






 Accepted: 02 April 2012  Published: 31 May 2012

Copyright © 2012 Author(s) retain the copyright of this article.
This article is published under the terms of the Creative Commons Attribution License 4.0


 

Recently, authors established a number of inequalities involving Khatri-Rao product of two positive matrices. Here, in this paper, the results are established in three ways. First, we find new Holder-type inequalities for Tracy-Singh and Khatri-Rao products of positive semi-definite matrices. Secondly, the results are extended to provide estimates of sums of the Khatri-Rao and Tracy-Singh products of any finite number of positive semi-definite matrices. Finally, the results lead to inequalities involving the Hadamard and Kronecker products, as a special case.

 

Key words: Tracy-Singh products, Khatri-Rao products, positive (semi) definite matrices, Holder inequalities


APA (2012). New Holder-type inequalities for the Tracy-Singh and Khatri-Rao products of positive matrices. International Journal of Computer Engineering Research, 3(3), 50 - 54.
Chicago Zeyad AL-Zhour. "New Holder-type inequalities for the Tracy-Singh and Khatri-Rao products of positive matrices." International Journal of Computer Engineering Research 3, no. 3 (2012): 50 - 54.
MLA Zeyad AL-Zhour. "New Holder-type inequalities for the Tracy-Singh and Khatri-Rao products of positive matrices." International Journal of Computer Engineering Research 3.3 (2012): 50 - 54.
   
DOI 10.5897/IJCER12.013
URL http://academicjournals.org/journal/IJCER/article-abstract/7C6247F8655

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