Affiliation:
1. Faculty of Economics and Business, University of Maribor, Razlagova 14, SI-2000 Maribor, SLOVENIA
Abstract
Abstract
Let ϕ be an injective, continuous, Lie product preserving map on Mn
(ℝ), n > 3. In the paper we show that then there exist an invertible matrix T ∈ Mn
(ℝ) and a continuous function ψ:Mn
(ℝ)→ ℝ, where ψ(A) = 0 for all matrices of trace zero, such that either ϕ(A) = TAT
−1 + ψ(A)I for all A ∈ Mn
(ℝ), or ϕ(A) = −TAtT−1 + ψ(A)I for all A ∈ Mn
(ℝ). We determine that a similar proposition holds true for the set Mn
(ℂ), n > 3.
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