  In this note we present a parameterized class of lower triangular matrices.
The components of the eigenvectors grow rapidly and will exceed the
representational range of any finite number system. The eigenvalues and the
eigenvectors are well-conditioned with respect to componentwise relative
perturbations of the matrix. This class of matrices is well suited for testing
software for computing eigenvectors as these routines must be able to handle
overflow successfully.
