Column ranks and their preservers over nonnegative real matrices.
The column rank of a matrix over the nonnegative reals is the least cardinality of the set of columns which span all columns over the nonnegative reals; the rank (also known as factor rank, Boolean rank, Schein rank, Barvinok rank) is the least \(k\) such that the given matrix is a product of \(m\times k\) and \(k\times n\) matrices. The authors determine those sizes of matrices for which the rank necessarily equals the column rank, and characterize linear operators which preserve the rank, and those which preserve the column rank, in various settings over the nonnegative reals.
scientific article; zbMATH DE number 2160177