
Given a zero/nonzero pattern or a sign pattern for a matrix, there is a 
range of possible ranks among the real matrices that exhibit this pattern. To 
know all ranks, it is generally sufficient to know the minimum rank (mr). But 
the mr is notoriously difficult to calculate. An interesting lower bound is the 
triangle minimum rank (tmr). Often tmr = mr, but not always. We discuss what 
can happen and give a scheme for computing mr in many cases. Several classical 
(such as projective planes) and new concepts come into play.
