The condition number of a regular (square) matrix is the product of
the norm of the matrix and the norm of its inverse (or
pseudo-inverse). More generally, the condition number is defined (also for
non-square matrices $A$) as
$$\kappa(A) = \frac{\max_{\|v\| = 1} \|A v\|}{\min_{\|v\| = 1} \|A v\|}.$$
Whenever x is not a square matrix, in our method
definitions, this is typically computed via rcond(qr.R(qr(X)), ...)
where X is x or t(x).
The condition number takes on values between 1 and infinity,
inclusive, and can be viewed as a factor by which errors in solving
linear systems with this matrix as coefficient matrix could be
magnified.
rcond() computes the reciprocal condition number
$1/\kappa$ with values in $[0,1]$ and can be viewed as a
scaled measure of how close a matrix is to being rank deficient (aka
singular).
Condition numbers are usually estimated, since exact computation is
costly in terms of floating-point operations. An (over) estimate of
reciprocal condition number is given, since by doing so overflow is
avoided. Matrices are well-conditioned if the reciprocal condition
number is near 1 and ill-conditioned if it is near zero.