Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 80878, 21 pages
doi:10.1155/JIA/2006/80878
Extension and generalization inequalities involving the Khatri-Rao product of several positive matrices
Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia (UPM), Serdang 43400, Selangor, Malaysia
Received 15 February 2005; Accepted 16 October 2005
Copyright © 2006 Zeyad Abdel Aziz Al Zhour and Adem Kilicman. 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.
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.