Gyrovector Spaces on the Open Convex Cone of Positive Definite Matrices
In this article we review an algebraic definition of the gyrogroup and a simplified version of the gyrovector space with two fundamental examples on the open ball of finite-dimensional Euclidean spaces, which are the Einstein and Möbius gyrovector spaces. We introduce the structure of gyrovecto...
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| Format: | Article |
| Language: | English |
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University of Kashan
2016-01-01
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| Series: | Mathematics Interdisciplinary Research |
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| Online Access: | https://mir.kashanu.ac.ir/article_13922_cb42b70fd53473b27d5c95a2db3e19ba.pdf |
| _version_ | 1797630978979528704 |
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| author | Sejong Kim |
| author_facet | Sejong Kim |
| author_sort | Sejong Kim |
| collection | DOAJ |
| description | In this article we review an algebraic definition of the gyrogroup and a simplified version of the gyrovector space with two fundamental examples on the open ball of finite-dimensional Euclidean spaces, which are the Einstein and Möbius gyrovector spaces. We introduce the structure of gyrovector space and the gyroline on the open convex cone of positive definite matrices and explore its interesting applications on the set of invertible density matrices. Finally we give an example of the gyrovector space on the unit ball of Hermitian matrices. |
| first_indexed | 2024-03-11T11:15:34Z |
| format | Article |
| id | doaj.art-7f1afd1715b94e8fa1dc6009ccbfcfcb |
| institution | Directory Open Access Journal |
| issn | 2476-4965 |
| language | English |
| last_indexed | 2024-03-11T11:15:34Z |
| publishDate | 2016-01-01 |
| publisher | University of Kashan |
| record_format | Article |
| series | Mathematics Interdisciplinary Research |
| spelling | doaj.art-7f1afd1715b94e8fa1dc6009ccbfcfcb2023-11-11T06:27:31ZengUniversity of KashanMathematics Interdisciplinary Research2476-49652016-01-011117318510.22052/mir.2016.1392213922Gyrovector Spaces on the Open Convex Cone of Positive Definite MatricesSejong Kim0Department of Mathematics, Chungbuk National University, Cheongju 28644, KoreaIn this article we review an algebraic definition of the gyrogroup and a simplified version of the gyrovector space with two fundamental examples on the open ball of finite-dimensional Euclidean spaces, which are the Einstein and Möbius gyrovector spaces. We introduce the structure of gyrovector space and the gyroline on the open convex cone of positive definite matrices and explore its interesting applications on the set of invertible density matrices. Finally we give an example of the gyrovector space on the unit ball of Hermitian matrices.https://mir.kashanu.ac.ir/article_13922_cb42b70fd53473b27d5c95a2db3e19ba.pdfgyrogroupgyrovector spacegyrolinegyromidpointpositive definite matrixdensity matrix |
| spellingShingle | Sejong Kim Gyrovector Spaces on the Open Convex Cone of Positive Definite Matrices Mathematics Interdisciplinary Research gyrogroup gyrovector space gyroline gyromidpoint positive definite matrix density matrix |
| title | Gyrovector Spaces on the Open Convex Cone of Positive Definite Matrices |
| title_full | Gyrovector Spaces on the Open Convex Cone of Positive Definite Matrices |
| title_fullStr | Gyrovector Spaces on the Open Convex Cone of Positive Definite Matrices |
| title_full_unstemmed | Gyrovector Spaces on the Open Convex Cone of Positive Definite Matrices |
| title_short | Gyrovector Spaces on the Open Convex Cone of Positive Definite Matrices |
| title_sort | gyrovector spaces on the open convex cone of positive definite matrices |
| topic | gyrogroup gyrovector space gyroline gyromidpoint positive definite matrix density matrix |
| url | https://mir.kashanu.ac.ir/article_13922_cb42b70fd53473b27d5c95a2db3e19ba.pdf |
| work_keys_str_mv | AT sejongkim gyrovectorspacesontheopenconvexconeofpositivedefinitematrices |