Convexity and concavity theorems on positive matrices and applications to geometric means and Khatri-rao products

Citation

Kilicman, Adem and Al Zhour, Zeyad Abdel Al Ziz (2005) Convexity and concavity theorems on positive matrices and applications to geometric means and Khatri-rao products. In: International Advanced Technology Congress: Conference on Advances in Theoretical Sciences, 6-8 Dec. 2005, Putrajaya, Malaysia. .

Abstract

This paper is concerned with two generalizations of Ando’s geometric mean and two related generalizations of the Tracy-Singh product for partitioned matrices. We recover the relationship between the Ando’s geometric mean and the Kronecker product to the case of operator mean and Tracy-Singh product. We provide several operator inequalities associated with non-negative linear maps by means of concavity and convexity theorems. We apply the concavity and convexity theorems in order to obtain new unusual estimates for the Khatri-Rao product positive definite matrices. Finally, the results lead inequalities involving Hadamard product and Ando’s (α − power) geometric mean, as a special case.

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Additional Metadata

Item Type:	Conference or Workshop Item (Paper)
Divisions:	Institute for Mathematical Research
Keywords:	Tracy-Singh product; Khatri-Rao product; Kronecker product; Hadamard product; Positive (semi) definite matrix; Ando’s geometric mean; α − geometric mean; Operator mean
Depositing User:	Erni Suraya Abdul Aziz
Date Deposited:	04 Jun 2015 04:21
Last Modified:	04 Jun 2015 04:21
URI:	http://psasir.upm.edu.my/id/eprint/38717
Statistic Details:	View Download Statistic

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