  We provide a determinantal formula for tau-functions of the KP hierarchy in
terms of rectangular, constant matrices $A$, $B$ and $C$ satisfying a rank one
condition. This result is shown to generalize and unify many previous results
of different authors on constructions of tau-functions for differential and
difference integrable systems from square matrices satisfying rank one
conditions. In particular, it contains as explicit special cases the formula of
Wilson for tau-functions of rational KP solutions in terms of Calogero-Moser
Lax matrices as well as our previous formula for KP tau functions in terms of
almost-intertwining matrices.
