ABSTRACT
In this paper, we address a problem left open by Wilkinson concerning the computation of the shortest (least squares) distance of any matrix A to a matrix  with at least one repeated eigenvalue. We have found that by casting the problem in a more geometric light, we can find an answer. This paper presents two methods which can identify  for a given A based on a geometric interpretation of the level sets of the eig function (considered as a multivalued differentiable function on the set of diagonalizable matrices). One method will be based, ultimately, on the examination of the pseudospectra of A. Additionally, relations will be given between the conditioning of the problem of  and the conditioning of the algorithms for solving that problem.
