Title: Total-positivity preservers,
Abstract: We prove that the only entrywise transforms of rectangular matrices which
preserve total positivity or total non-negativity are either constant or
linear. This follows from an extended classification of preservers of these two
properties for matrices of fixed dimension. We also prove that the same
assertions hold upon working only with symmetric matrices; for total-positivity
preservers our proofs proceed through solving two totally positive completion
problems.