Matrix functions and applications: Part IV — Matrix functions and constituent matrices

This fourth part of a five-part series starts with the expansion of an analytic function of an arbitrary square matrix, involving real or complex numbers, in terms of its constituent matrices. The conjoint matrix and characteristic polynominal are computed by a convenient algorithm and are then used for calculating constituent matrices. Finally there is a discussion of the two-sided matrix equation AY + B = YC, and of the reduction of an arbitrary matrix to a similar Jordan matrix.