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On preservers of determinant over a field

Kalinowski J.

Demonstratio Mathematica

2008

Vol. 41, nr 3

519-524

Operators preserving the determinant of real matrices were studied in [1], [2] and [5] under assumption that the operator is linear. In this paper the linearity of the operators is not assumed: we only assume that the operators are of the form F = [fi,j], where functions fij : [...], we characterize these operators from [...] into itself preserving the determinant. An operator preserving the determinant of matrices must be linear as in [4]. The form of operator F is presented.