  Consider an N x N matrix A for which zero is a defective eigenvalue. In this
case, the algebraic multiplicity of the zero eigenvalue is greater than the
geometric multiplicity. We show how an inflated (N+1) x (N+1) matrix L can be
constructed as a rank one perturbation to A, such that L is singular but no
longer defective, and the nullvectors of L can be easily related to the
nullvectors of A. The motivation for this construction comes from linear
stability analysis of an experimental reaction-diffusion system which exhibits
the Turing instability. The utility of this scheme is accurate numerical
computation of nullvector(s) corresponding to a defective zero eigenvalue. We
show that numerical computations on L yield more accurate eigenvectors than
direct computation on A.
