  In this paper, we establish a general setup for studying incidence-preserving
motions of projective geometric configurations of points and lines via a
"projective rigidity matrix". The spaces of infinitesimal motions of a
point-line configuration and dependencies amongst the point-line incidences can
be interpreted as the kernel and co-kernel of this projective rigidity matrix,
respectively. We also introduce a symmetry-adapted projective rigidity matrix
for analysing symmetric configurations and their symmetry-preserving motions.
The symmetry may be a point group or a more general symmetry, such as an
autopolarity.
