Yes. It is. (the number of nonzero singular values, that is)
Also, rank is the dimension of the space spanned by a matrix. The rank of
the outer product of two vectors is 1 (except when one of them is zero).
The sum of two independent matrices with rank k_1 and k_2 is k_1 + k_2.
Independent means that the spaces that they span share only the origin.
You can view SVD as finding the most important dimensions of the span of a
matrix. You can also view the SVD as a sum of rank one matrices formed by
the outer products of the corresponding left and right singular vectors.
Since the singular vectors are orthonormal, their outer products are
independent and thus the sum of k such outer products has rank k.
If you view SVD as compressing the information in a matrix, then the rank of
the result is a reasonable measure of how much information remains.
On Tue, Jul 6, 2010 at 12:15 PM, Grant Ingersoll <gsingers@apache.org>wrote:
> Question: What exactly is the rank, anyway? It's the number of singular
> values, right?
>
