Year: 2009
Type: article
Abstract: Operators preserving singularity and nonsingularity of matrices were studied in paper of P. Botta under the assumption that operators are linear.In the present paper the linearity of operators is not assumed: we only assume that operators are of the form T = (fi,j), where fij : K -• K and K is a field, i,j € {1,2, ...,n}.If n > 3, then in the matrix space M n (K) operators preserving singularity and nonsingularity of matrices must be as in paper of P. Botta.If n < 2, operators may be nonlinear.In this case the forms of the operators are presented.Let R, N denote the set of real numbers or positive integer numbers, respectively.Let M n (K) be the set of n x n matrices over a field K, i.e.
Source: Demonstratio Mathematica
Author: Józef Kalinowski
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,187
OpenAlex ID: W1200428284