  A rigidity theory is developed for bar-joint frameworks in linear matrix
spaces endowed with a unitarily invariant norm. Analogues of Maxwell's counting
criteria are obtained and minimally rigid matrix frameworks are shown to belong
to the matroidal class of (k,l)-sparse graphs for suitable k and l. A
characterisation of infinitesimal rigidity is obtained for product norms and it
is shown that K_6 - e (respectively, K_7) is the smallest minimally rigid graph
for the class of 2 x 2 symmetric (respectively, hermitian) matrices with the
trace norm.
