SJSU Singular Matrix Database

### The calculated gap in the singular values

If the calculated numerical rank
of A is numrank and if the calculated singular values are
svals(1), svals(2), . . . then

gap = svals(numrank) / svals(numrank+1).

For an m by n matrix A note that svals(numrank+1) is smaller than
our default tolerance max(m,n) * eps(norm(A)) and, as discussed
here, svals(numrank+1) may have little relative
accuracy. Consequently the calculated gap may also have little relative accuracy.
Even so, the calculated gap is often useful to help determine if the numerical rank is
well defined. See this link.