Linear maps preserving the Cullis' determinant. II

Alexander Guterman; Andrey Yurkov

Paper

Linear maps preserving the Cullis' determinant. II

Abstract

This paper is the second in the series of papers devoted to the explicit description of linear maps preserving the Cullis' determinant of rectangular matrices with entries belonging to an arbitrary ground field which is large enough. In this part we solve the linear preserver problem for the Cullis' determinant defined on the spaces of matrices of size

with

and

is odd. In comparison with the case when

is even, in this case linear maps preserving the Cullis' determinant could be singular and are represented as a sum of two linear maps: first is two-sided matrix multiplication and second is any linear map whose image consists of matrices, all rows of which are equal.