http://hdl.handle.net/20.500.12128/465
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. |
URI: | http://hdl.handle.net/20.500.12128/465 |
ISSN: | 0860-2107 |
Appears in Collections: | Artykuły (WNŚiT) |
File | Description | Size | Format | |
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Kalinowski_On_invertible_preservers_of_singularity.pdf | 677,58 kB | Adobe PDF | View/Open |
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