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A rigidity theory is developed for bar-joint frameworks in linear matrixspaces endowed with a unitarily invariant norm. Analogues of Maxwell's countingcriteria are obtained and minimally rigid matrix frameworks are shown to belongto the matroidal class of (k,l)-sparse graphs for suitable k and l. Acharacterisation of infinitesimal rigidity is obtained for product norms and itis shown that K_6 - e (respectively, K_7) is the smallest minimally rigid graphfor the class of 2 x 2 symmetric (respectively, hermitian) matrices with thetrace norm.

Graph rigidity for unitarily invariant matrix norms