IJPAM: Volume 60, No. 3 (2010)
MATRICES FORCES THE LINEARITY
Department of Mathematics
Silesian University
14, Ul. Bankowa, Katowice, 40-007, POLAND
e-mail: kalinows@ux2.math.us.edu.pl
Abstract.Operators preserving the rank of
real matrices were studied in Basley [#!2!#] under assumption that the
operator is linear. In the present paper the linearity of the
operator is not assumed: we assume only that the operator is of
the form , where
are functions
for
. If the min{
, then in the matrix space
the operator preserving the rank of matrices must be
linear as in Basley [#!2!#]. If the min
, then the operator may be
nonlinear. In both cases the forms of the operator are presented.
Received: February 11, 2010
AMS Subject Classification: 15A03
Key Words and Phrases: rank of matrices, preservers
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 60
Issue: 3