On determinant preserver problems
โ Scribed by Victor Tan; Fei Wang
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 86 KB
- Volume
- 369
- Category
- Article
- ISSN
- 0024-3795
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โฆ Synopsis
Let M n and T n be the vector spaces of n ร n matrices and upper triangular matrices over a field F (with some cardinality and characteristic restrictions) respectively. We characterise transformations ฯ on these two spaces separately which satisfy one of the following conditions:
- det(A + ฮปB) = det(ฯ(A) + ฮปฯ(B)) for all A, B and ฮป. 2. ฯ is surjective and det(A + ฮปB) = det(ฯ(A) + ฮปฯ(B)) for all A, B and two specific ฮป. 3. ฯ is additive and preserves determinant.
๐ SIMILAR VOLUMES
In this article we classify rank-one nonincreasing maps ฯ on n-square block triangular matrix algebras with the assumption that ฯ(I n ) is of rank n. As applications, we obtain complete classifications of adjugate-commuting maps, and compound-commuting maps on block triangular matrix algebras.
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