The simple theory behind the design of magnetic film matrices is presented, and it is shown that complete cycles representing switching operations can be traced out on diagrams of critical field values. Three known modes of operation are illustrated in the diagrams, and new ones are derived from the diagrams which use more than one film element per bit to combat troubles caused by film misorientation. The magnetization rotations expected in four modes are illustrated, together with the associated waveforms in the corresponding matrices. Figures of merit are derived for the tolerances to variations in digit current and in film orientation for the useful situation where the word current is high, both for the simplest theoretical model and for more realistic cases. The new modes of operation are found to be the most tolerant.