On the reduction of rank of linear differential systems
Donald A. Lutz · Pacific Journal of Mathematics · 1972
The rank of a linear differential system in the neighborhood of a pole of the system is defined to be one less than the order of the pole of the coefficient matrix of the system.H. L. Turrittin has shown that arbitrary rank can be reduced to rank one at the expense of increasing the dimension of the system in proportion to the amount of reduction.Can this procedure lead to extraneous solutions of the rank-reduced system which differ in behavior from solutions of the given system?This question is answered by a transformation of the rank-reduced system to a block-diagonal form, exhibiting the precise relation between solutions of the two systems.In particular, if the original system has a regular singularity at the pole in question, then so does the rank-reduced system.