On invertible preservers of singularity and nonsingularity of matrices over a field
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.
Keywords
invertible preservers of singularity or nonsingularity of matrices
References
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Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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