✦ LIBER ✦

On determinant preserver problems

✍ Scribed by Victor Tan; Fei Wang

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 86 KB
Volume: 369
Category: Article
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(02)00739-5

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✦ Synopsis

Let M n and T n be the vector spaces of n × n matrices and upper triangular matrices over a field F (with some cardinality and characteristic restrictions) respectively. We characterise transformations φ on these two spaces separately which satisfy one of the following conditions:

det(A + λB) = det(φ(A) + λφ(B)) for all A, B and λ. 2. φ is surjective and det(A + λB) = det(φ(A) + λφ(B)) for all A, B and two specific λ. 3. φ is additive and preserves determinant.

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