AbstractOne very natural way of describing industrial processes with interference gives rise to particularly unwieldy mathematical expressions; but by a change of language, these expressions can be simply handled by the familiar notation of matrix algebra-where, however, addition and multiplication do not have their usual arithmetical meanings. This line of attack promises to produce a useful machinery for the analysis of systems of interacting processes, but first all the usual algebraic questions must be answered-e.g. the question of evaluating the eigenvalues and eigenvectors of a matrix in the new notation. This problem is equivalent to that of determining the steady states of a system of interacting processes, assuming constant activity times. This paper shows that the eigenvalue of a general matrixAcan be determined explicitly in terms ofA, as can the eigenvector in a particular set of cases. The general eigenvector and eigenvalue computation problem can be simplified into a dual form closely analogous to a formulation of the Assignment Problem by H. W. Kuhn.