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Title: On invertible preservers of singularity and nonsingularity of matrices over a field
Authors: Kalinowski, Józef
Keywords: Invertible Preservers of Singularity; Nonsingularity of Matrices
Issue Date: 2010
Citation: Annales Mathematicae Silesianae, Nr 24 (2010), s. 27-33
Abstract: Invertible operators preserving singularity of matrices were studied in [3] and [4] under assumption that operators are linear. In the present paper the linearity of operators is not assumed: we assume only that operators are of the form F = (fi,j), where fi,j : F −> F and F is a field, i, j {1, 2, . . . , n}. If n ≥ 3, then in the matrix space Mn(F) operators preserving singularity of matrices must be as in [1]. If n ≤ 2, then operators may be nonlinear. In this case the forms of the operators are presented.
ISSN: 0860-2107
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