Khatri-Rao Products for Operator Matrices Acting on the Direct Sum of Hilbert Spaces
We introduce the notion of Khatri-Rao product for operator matrices acting on the direct sum of Hilbert spaces. This notion generalizes the tensor product and Hadamard product of operators and the Khatri-Rao product of matrices. We investigate algebraic properties, positivity, and monotonicity of th...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2016/8301709 |
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| _version_ | 1849309091803955200 |
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| author | Arnon Ploymukda Pattrawut Chansangiam |
| author_facet | Arnon Ploymukda Pattrawut Chansangiam |
| author_sort | Arnon Ploymukda |
| collection | DOAJ |
| description | We introduce the notion of Khatri-Rao product for operator matrices acting on the direct sum of Hilbert spaces. This notion generalizes the tensor product and Hadamard product of operators and the Khatri-Rao product of matrices. We investigate algebraic properties, positivity, and monotonicity of the Khatri-Rao product. Moreover, there is a unital positive linear map taking Tracy-Singh products to Khatri-Rao products via an isometry. |
| format | Article |
| id | doaj-art-0c87b3daf72d40b88a507393e8a1a69b |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-0c87b3daf72d40b88a507393e8a1a69b2025-08-20T03:54:15ZengWileyJournal of Mathematics2314-46292314-47852016-01-01201610.1155/2016/83017098301709Khatri-Rao Products for Operator Matrices Acting on the Direct Sum of Hilbert SpacesArnon Ploymukda0Pattrawut Chansangiam1Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Chalongkrung Rd., Bangkok 10520, ThailandDepartment of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Chalongkrung Rd., Bangkok 10520, ThailandWe introduce the notion of Khatri-Rao product for operator matrices acting on the direct sum of Hilbert spaces. This notion generalizes the tensor product and Hadamard product of operators and the Khatri-Rao product of matrices. We investigate algebraic properties, positivity, and monotonicity of the Khatri-Rao product. Moreover, there is a unital positive linear map taking Tracy-Singh products to Khatri-Rao products via an isometry.http://dx.doi.org/10.1155/2016/8301709 |
| spellingShingle | Arnon Ploymukda Pattrawut Chansangiam Khatri-Rao Products for Operator Matrices Acting on the Direct Sum of Hilbert Spaces Journal of Mathematics |
| title | Khatri-Rao Products for Operator Matrices Acting on the Direct Sum of Hilbert Spaces |
| title_full | Khatri-Rao Products for Operator Matrices Acting on the Direct Sum of Hilbert Spaces |
| title_fullStr | Khatri-Rao Products for Operator Matrices Acting on the Direct Sum of Hilbert Spaces |
| title_full_unstemmed | Khatri-Rao Products for Operator Matrices Acting on the Direct Sum of Hilbert Spaces |
| title_short | Khatri-Rao Products for Operator Matrices Acting on the Direct Sum of Hilbert Spaces |
| title_sort | khatri rao products for operator matrices acting on the direct sum of hilbert spaces |
| url | http://dx.doi.org/10.1155/2016/8301709 |
| work_keys_str_mv | AT arnonploymukda khatriraoproductsforoperatormatricesactingonthedirectsumofhilbertspaces AT pattrawutchansangiam khatriraoproductsforoperatormatricesactingonthedirectsumofhilbertspaces |