`Frank' is a Hessenberg, matrix
with ill conditioned
eigenvalues, whose determinant is 1.
The elements may be optionally reflected about the
The matrix has all positive eigenvalues and they occur in reciprocal
pairs (so that 1 is an eigenvalue if the order is odd). The eigenvalues
may be obtained in terms of the zeros of the Hermite polynomials.
The smallest half of the eigenvalues are ill conditioned,
the more so for larger order.
This version incorporates improvements suggested by W. Kahan.