Factorization of Triangular Matrix Functions

Finding the factors and partial indices in the factorization of a matrix function relative to a contour is in general a very complicated problem. For many special cases it is possible to obtain explicit factorizations. One of these cases is the case of triangular matrix functions. This chapter discusses the general triangular case and studies in full detail the theory in the 2 × 2-matrix case. An important type of “mixed triangular” matrix function appears on disconnected contours where on each component the matrix function is of different (upper or lower) triangular type. The problem of factorization of these “mixed triangular” matrix function is related to the classical concept of the resultant of a pair of (polynomial) functions.