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....
| 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 |
| _version_ | 1796973399407329280 |
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| author | Kilicman, Adem Al Zhour, Zeyad Abdel Al Ziz |
| author_facet | Kilicman, Adem Al Zhour, Zeyad Abdel Al Ziz |
| author_sort | Kilicman, Adem |
| collection | UPM |
| description | 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. |
| first_indexed | 2024-03-06T08:42:05Z |
| format | Conference or Workshop Item |
| id | upm.eprints-38717 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T08:42:05Z |
| publishDate | 2005 |
| record_format | dspace |
| spelling | upm.eprints-387172015-06-04T04:21:17Z http://psasir.upm.edu.my/id/eprint/38717/ Convexity and concavity theorems on positive matrices and applications to geometric means and Khatri-rao products Kilicman, Adem Al Zhour, Zeyad Abdel Al Ziz 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. 2005 Conference or Workshop Item NonPeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/38717/1/38717.pdf 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. . |
| spellingShingle | Kilicman, Adem Al Zhour, Zeyad Abdel Al Ziz Convexity and concavity theorems on positive matrices and applications to geometric means and Khatri-rao products |
| title | Convexity and concavity theorems on positive matrices and applications to geometric means and Khatri-rao products |
| title_full | Convexity and concavity theorems on positive matrices and applications to geometric means and Khatri-rao products |
| title_fullStr | Convexity and concavity theorems on positive matrices and applications to geometric means and Khatri-rao products |
| title_full_unstemmed | Convexity and concavity theorems on positive matrices and applications to geometric means and Khatri-rao products |
| title_short | Convexity and concavity theorems on positive matrices and applications to geometric means and Khatri-rao products |
| title_sort | convexity and concavity theorems on positive matrices and applications to geometric means and khatri rao products |
| url | http://psasir.upm.edu.my/id/eprint/38717/1/38717.pdf |
| work_keys_str_mv | AT kilicmanadem convexityandconcavitytheoremsonpositivematricesandapplicationstogeometricmeansandkhatriraoproducts AT alzhourzeyadabdelalziz convexityandconcavitytheoremsonpositivematricesandapplicationstogeometricmeansandkhatriraoproducts |