Symbolic Computation Group

We study the solutions of the matrix equation S exp(S) = A where S and A are matrices, equations which arise naturally in the study of delay differential equations y'(t) = A y(t).

The talk will concentrate on the distinction between evaluating a matrix function and solving a matrix equation. In particular, we will show that the matrix Lambert W function evalauted at the matrix A does not represent all possible solutions to the matrix equation S exp(S) = A. The results themselves can be extended to more general matrix equations.