The `Kahan' matrix is an upper trapezoidal matrix that has some
interesting properties regarding estimation of condition and rank.

To ensure that the QR factorization with column pivoting does not
interchange columns in the presence of rounding errors, the diagonal
elements are perturbed by PERTURBATION*EPSILON*(N+1-i), where
EPSILON is the double precision epsilon.
The default value of the perturbation (25) ensures no interchanges
up to at least N = 90 in IEEE arithmetic, for the default value
of Theta (1.2).
For square matrices, the inverse is known explicitly
and can be computed here.