Institution: Stanford University, Department of Computer Science

Title: Note on the practical significance of the Drazin inverse

Author: Wilkinson, James Hardy

Date: April 1979

Abstract: The solution of the differential system Bx = Ax + f where A and B are n x n matrices and A - $\lambda$B is not a singular pencil may be expressed in terms of the Drazin inverse. It is shown that there is a simple reduced form for the pencil A - $\lambda$B which is adequate for the determination of the general solution and that although the Drazin inverse could be determined efficiently from this reduced form it is inadvisable to do so.

http://i.stanford.edu/pub/cstr/reports/cs/tr/79/736/CS-TR-79-736.pdf