Open Access

Extension and generalization inequalities involving the Khatri-Rao product of several positive matrices

Journal of Inequalities and Applications20062006:80878

DOI: 10.1155/JIA/2006/80878

Received: 15 February 2005

Accepted: 16 October 2005

Published: 25 June 2006

Abstract

Recently, there have been many authors, who established a number of inequalities involving Khatri-Rao and Hadamard products of two positive matrices. In this paper, the results are established in the following three ways. First, we find generalization of the inequalities involving Khatri-Rao product using results given by Liu (1999), Mond and Pečarić (1997), Cao et al. (2002), Chollet (1997), and Visick (2000). Second, we recover and develop some results of Visick. Third, the results are extended to the case of Khatri-Rao product of any finite number of matrices. These results lead to inequalities involving Hadamard product, as a special case.

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Authors’ Affiliations

(1)
Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia (UPM)

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Copyright

© Z.A. Al Zhour and A. Kilicman. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.