Some Properties of the Souriau–Frame Algorithm with Application to the Inversion of Rational Matrices
T. Downs · SIAM Journal on Applied Mathematics · 1975
All terms generated during the process of inversion of the matrix $[ {sI - A} ]$ by the Souriau–Frame algorithm are expressed as functions of minors of the matrix A. This information is used to generate an algorithm for the inversion of a matrix of rational functions. The algorithm produces an inverse which is devoid of redundant factors if there are no factors common to any pair of polynomials in the matrix to be inverted. This condition will not generally be met, and an approach to the removal of redundancy from the solution is also discussed.