Convexity and concavity theorems on positive matrices and applications to geometric means and Khatri-rao products
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....
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| Main Authors: | , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
2005
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| Online Access: | http://psasir.upm.edu.my/id/eprint/38717/1/38717.pdf http://psasir.upm.edu.my/id/eprint/38717/ |
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| Summary: | 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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