Geodesic
Nonlinear maps preserving the elementary symmetric functions
Ars Mathematica Contemporanea, Tome 21 (2021) no. 1, article no. 09, 8 p.

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Let ℳn be the algebra of all n × n complex matrices, and for a natural number 2 ≤ k ≤ n denote by Ek(x) the kth elementary symmetric function on the eigenvalues of x ∈ ℳn. For two maps φ, ψ: ℳn → ℳn, one of them being surjective, we prove that if Ek(λx + y) = Ek(λφ(x) + ψ(y)) for each λ ∈ C and x, y ∈ ℳn, then φ = ψ on ℳn, the common value being a linear map from ℳn into itself. In particular, for 3 ≤ k ≤ n the general form of φ and ψ can be computed explicitly.
DOI : 10.26493/1855-3974.2488.f5c
Keywords: Elementary symmetric function, nonlinear, preserver 
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Constantin Costara. Nonlinear maps preserving the elementary symmetric functions. Ars Mathematica Contemporanea, Tome 21 (2021) no. 1, article  no. 09, 8 p. doi : 10.26493/1855-3974.2488.f5c. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2488.f5c/

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