If we have a matrix M, we can always make a singular value decomposition. If the matrix has full column rank (= is invertible), then the singular values are all nonzero, otherwise they are not all nonzero.
Now, we can also associate a condition number to a matrix given by
cond(M) = s1/sk
where k is min(m, n) (where M is a m times n matrix). If M is rectangular, then it is not invertible, so the condition number should be infinite.
Now, when I find the condition number of a rectangular matrix in MatLAB, it gives me a (large) number, which is finite. How can that be?