n all rank-revealing decompositions, it would be nice to have a function to construct the kernel matrix for a prescribed dimension of the kernel. At the very least for SVD decompositions, where this would just be taking the n singular vectors associated to the n smallest singular values. In real-world use cases, this is the most useful way to get the kernel. The same idea should then be applied to image() for good measure.
Then again, with the new SVD that we've been discussing, we'd get that for free (computation/application of U and V on demand).
Bug 593 is related and should be solved to make this useful.