Additive preservers of rank-additivity on matrix spaces
Let F be a field. Let V denote the vector space of all m x n matrices over F or the vector space of all n x n symmetric matrices over F of characteristic not 2 or 3. For each fixed positive integer s >= 2, let Qs denote the set of all matrix pairs (A, B) in V such that rank(A + B) = rank(A) + ran...
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| Format: | Article |
| Language: | English |
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2005
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| Online Access: | http://shdl.mmu.edu.my/2229/ http://shdl.mmu.edu.my/2229/1/1537.pdf |
| _version_ | 1848789998847918080 |
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| author | CHOOI, W LIM, M |
| author_facet | CHOOI, W LIM, M |
| author_sort | CHOOI, W |
| building | MMU Institutional Repository |
| collection | Online Access |
| description | Let F be a field. Let V denote the vector space of all m x n matrices over F or the vector space of all n x n symmetric matrices over F of characteristic not 2 or 3. For each fixed positive integer s >= 2, let Qs denote the set of all matrix pairs (A, B) in V such that rank(A + B) = rank(A) + rank(B) <= s. We characterize additive mappings psi on V such that (psi(A), psi (B)) epsilon Qs whenever (A, B) epsilon Qs for a fixed s. We also describe the structure of linear mappings from the space of n x n matrices over F to the space of p x q matrices over F that preserve rank-additivity, where char F not equal 2. (c) 2005 Elsevier Inc. All rights reserved. |
| first_indexed | 2025-11-14T18:05:38Z |
| format | Article |
| id | mmu-2229 |
| institution | Multimedia University |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T18:05:38Z |
| publishDate | 2005 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | mmu-22292011-08-12T01:33:14Z http://shdl.mmu.edu.my/2229/ Additive preservers of rank-additivity on matrix spaces CHOOI, W LIM, M QA Mathematics Let F be a field. Let V denote the vector space of all m x n matrices over F or the vector space of all n x n symmetric matrices over F of characteristic not 2 or 3. For each fixed positive integer s >= 2, let Qs denote the set of all matrix pairs (A, B) in V such that rank(A + B) = rank(A) + rank(B) <= s. We characterize additive mappings psi on V such that (psi(A), psi (B)) epsilon Qs whenever (A, B) epsilon Qs for a fixed s. We also describe the structure of linear mappings from the space of n x n matrices over F to the space of p x q matrices over F that preserve rank-additivity, where char F not equal 2. (c) 2005 Elsevier Inc. All rights reserved. 2005-06 Article NonPeerReviewed application/pdf en http://shdl.mmu.edu.my/2229/1/1537.pdf CHOOI, W and LIM, M (2005) Additive preservers of rank-additivity on matrix spaces. Linear Algebra and its Applications, 402. pp. 291-302. ISSN 00243795 http://dx.doi.org/10.1016/j.laa.2005.01.020 doi:10.1016/j.laa.2005.01.020 doi:10.1016/j.laa.2005.01.020 |
| spellingShingle | QA Mathematics CHOOI, W LIM, M Additive preservers of rank-additivity on matrix spaces |
| title | Additive preservers of rank-additivity on matrix spaces |
| title_full | Additive preservers of rank-additivity on matrix spaces |
| title_fullStr | Additive preservers of rank-additivity on matrix spaces |
| title_full_unstemmed | Additive preservers of rank-additivity on matrix spaces |
| title_short | Additive preservers of rank-additivity on matrix spaces |
| title_sort | additive preservers of rank-additivity on matrix spaces |
| topic | QA Mathematics |
| url | http://shdl.mmu.edu.my/2229/ http://shdl.mmu.edu.my/2229/ http://shdl.mmu.edu.my/2229/ http://shdl.mmu.edu.my/2229/1/1537.pdf |