Linear spaces and preservers of persymmetric triangular matrices of bounded rank-two / Ng Zhen Chuan
Let F be a field and n an integer > 2. We say that a square matrix A is persymmetric if A is symmetric in the second diagonal. Let STn(F) denote the linear space of all n x n persymmetric upper triangular matrices over F. A subspace S of STn(F) is said to be a space of bounded rank-two matrices i...
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| Format: | Thesis |
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2012
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| Online Access: | http://studentsrepo.um.edu.my/4547/ http://studentsrepo.um.edu.my/4547/1/DISSERTATION_%2D_SGP_100007.pdf |
| _version_ | 1848772657007296512 |
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| author | Ng, Zhen Chuan |
| author_facet | Ng, Zhen Chuan |
| author_sort | Ng, Zhen Chuan |
| building | UM Research Repository |
| collection | Online Access |
| description | Let F be a field and n an integer > 2. We say that a square matrix A is persymmetric if A is symmetric in the second diagonal. Let STn(F) denote the linear space of all n x n persymmetric upper triangular matrices over F. A subspace S of STn(F) is said to be a space of bounded rank-two matrices if each matrix in S has rank bounded above by two, and a rank-two space if each nonzero element in it has rank two.
In this dissertation, we classify subspaces of bounded rank-two matrices of STn(F) over a field F with at least three elements. As a corollary, a complete description
of rank-two subspaces of STn(F) is obtained. We next deduce from the structural results of subspaces of bounded rank-two matrices of STn(F), a characterization of
linear maps � : STn(F) ! STm(F), m > n > 2, that send nonzero matrices with rank at most two to nonzero matrices with rank at most two. |
| first_indexed | 2025-11-14T13:29:59Z |
| format | Thesis |
| id | um-4547 |
| institution | University Malaya |
| institution_category | Local University |
| last_indexed | 2025-11-14T13:29:59Z |
| publishDate | 2012 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | um-45472014-10-17T02:24:45Z Linear spaces and preservers of persymmetric triangular matrices of bounded rank-two / Ng Zhen Chuan Ng, Zhen Chuan Q Science (General) QA Mathematics Let F be a field and n an integer > 2. We say that a square matrix A is persymmetric if A is symmetric in the second diagonal. Let STn(F) denote the linear space of all n x n persymmetric upper triangular matrices over F. A subspace S of STn(F) is said to be a space of bounded rank-two matrices if each matrix in S has rank bounded above by two, and a rank-two space if each nonzero element in it has rank two. In this dissertation, we classify subspaces of bounded rank-two matrices of STn(F) over a field F with at least three elements. As a corollary, a complete description of rank-two subspaces of STn(F) is obtained. We next deduce from the structural results of subspaces of bounded rank-two matrices of STn(F), a characterization of linear maps � : STn(F) ! STm(F), m > n > 2, that send nonzero matrices with rank at most two to nonzero matrices with rank at most two. 2012 Thesis NonPeerReviewed application/pdf http://studentsrepo.um.edu.my/4547/1/DISSERTATION_%2D_SGP_100007.pdf Ng, Zhen Chuan (2012) Linear spaces and preservers of persymmetric triangular matrices of bounded rank-two / Ng Zhen Chuan. Masters thesis, University of Malaya. http://studentsrepo.um.edu.my/4547/ |
| spellingShingle | Q Science (General) QA Mathematics Ng, Zhen Chuan Linear spaces and preservers of persymmetric triangular matrices of bounded rank-two / Ng Zhen Chuan |
| title | Linear spaces and preservers of persymmetric triangular matrices of bounded rank-two / Ng Zhen Chuan |
| title_full | Linear spaces and preservers of persymmetric triangular matrices of bounded rank-two / Ng Zhen Chuan |
| title_fullStr | Linear spaces and preservers of persymmetric triangular matrices of bounded rank-two / Ng Zhen Chuan |
| title_full_unstemmed | Linear spaces and preservers of persymmetric triangular matrices of bounded rank-two / Ng Zhen Chuan |
| title_short | Linear spaces and preservers of persymmetric triangular matrices of bounded rank-two / Ng Zhen Chuan |
| title_sort | linear spaces and preservers of persymmetric triangular matrices of bounded rank-two / ng zhen chuan |
| topic | Q Science (General) QA Mathematics |
| url | http://studentsrepo.um.edu.my/4547/ http://studentsrepo.um.edu.my/4547/1/DISSERTATION_%2D_SGP_100007.pdf |