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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 / Synopsis

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 12:21
Last Modified: 04 Jun 2015 12:21
URI: http://psasir.upm.edu.my/id/eprint/38717
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