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Matrix modelling: Exploiting common patterns in constraint programming

Constraint programs with one or more matrices of decision variables are commonly and naturally used to model real-world problems. We call these matrix models and claim that they can be studied beneficially as a class. In support of this claim we present results in three areas: the systematization of formulating matrix models, the elimination of row and column symmetries from matrix models, and the efficient implementation of constraints for channelling between matrices.