Matrices with all minors of some fixed order being equal: the rank, dimension and characteristic property

Abstract

Investigated in this paper is a
class $\mathfrak{M}$ of matrices (over an arbitrary field) in which
all minors of some fixed order $k$ are equal and nonzero. It is
established that the rank of such matrices equals to $k$. The
possible values for the dimension of a matrix in $\mathfrak{M}$ are
found. A necessary and sufficient condition for a matrix to belong
to the class $\mathfrak{M}$ is also given.