On classical adjoint-commuting mappings between matrix algebras
Let F be a field and let m and n be integers with m, n >= 3. Let M(n) denote the algebra of n x n matrices over F. In this note, we characterize mappings psi : M(n) -> M(m) that satisfy one of the following conditions: 1. vertical bar F vertical bar = 2 or vertical bar F vertical bar > n +...
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| Format: | Article |
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Elsevier
2010
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| _version_ | 1825720573224812544 |
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| author | Chooi, W.L. Ng, W.S. |
| author_facet | Chooi, W.L. Ng, W.S. |
| author_sort | Chooi, W.L. |
| collection | UM |
| description | Let F be a field and let m and n be integers with m, n >= 3. Let M(n) denote the algebra of n x n matrices over F. In this note, we characterize mappings psi : M(n) -> M(m) that satisfy one of the following conditions: 1. vertical bar F vertical bar = 2 or vertical bar F vertical bar > n + 1, and psi (adj (A + alpha B)) = adj (psi (A) + alpha psi (B)) for all A, B is an element of M(n) and alpha is an element of F with psi (I(n)) not equal 0. 2. psi is surjective and psi (adj (A - B)) = adj (psi (A) - psi (B)) for every A, B is an element of M(n). Here, adj A denotes the classical adjoint of the matrix A, and I(n) is the identity matrix of order n. We give examples showing the indispensability of the assumption psi (I(n)) not equal 0 in our results. (C) 2009 Elsevier Inc. All rights reserved. |
| first_indexed | 2024-03-06T05:37:10Z |
| format | Article |
| id | um.eprints-14730 |
| institution | Universiti Malaya |
| last_indexed | 2024-03-06T05:37:10Z |
| publishDate | 2010 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | um.eprints-147302015-11-11T03:15:40Z http://eprints.um.edu.my/14730/ On classical adjoint-commuting mappings between matrix algebras Chooi, W.L. Ng, W.S. Q Science (General) Let F be a field and let m and n be integers with m, n >= 3. Let M(n) denote the algebra of n x n matrices over F. In this note, we characterize mappings psi : M(n) -> M(m) that satisfy one of the following conditions: 1. vertical bar F vertical bar = 2 or vertical bar F vertical bar > n + 1, and psi (adj (A + alpha B)) = adj (psi (A) + alpha psi (B)) for all A, B is an element of M(n) and alpha is an element of F with psi (I(n)) not equal 0. 2. psi is surjective and psi (adj (A - B)) = adj (psi (A) - psi (B)) for every A, B is an element of M(n). Here, adj A denotes the classical adjoint of the matrix A, and I(n) is the identity matrix of order n. We give examples showing the indispensability of the assumption psi (I(n)) not equal 0 in our results. (C) 2009 Elsevier Inc. All rights reserved. Elsevier 2010 Article PeerReviewed Chooi, W.L. and Ng, W.S. (2010) On classical adjoint-commuting mappings between matrix algebras. Linear Algebra and its Applications, 432 (10). pp. 2589-2599. |
| spellingShingle | Q Science (General) Chooi, W.L. Ng, W.S. On classical adjoint-commuting mappings between matrix algebras |
| title | On classical adjoint-commuting mappings between matrix algebras |
| title_full | On classical adjoint-commuting mappings between matrix algebras |
| title_fullStr | On classical adjoint-commuting mappings between matrix algebras |
| title_full_unstemmed | On classical adjoint-commuting mappings between matrix algebras |
| title_short | On classical adjoint-commuting mappings between matrix algebras |
| title_sort | on classical adjoint commuting mappings between matrix algebras |
| topic | Q Science (General) |
| work_keys_str_mv | AT chooiwl onclassicaladjointcommutingmappingsbetweenmatrixalgebras AT ngws onclassicaladjointcommutingmappingsbetweenmatrixalgebras |