On invertible preservers of singularity and nonsingularity of matrices over a field - Kalinowski, Józef (Annales Mathematicae Silesianae, 2010)
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 : ????→???? and ???? is a field, i,j∈1, 2, . . . , n. If n≥3, then in the matrix space Mn(????) 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.