### The SVD

The SVD of a protein conformation matrix is similar to a quasi-normal
mode analysis in that it gives a set of vectors, called the left
singular vector, which describe which direction each atom prefers to
move in. The SVD also gives temporal information through the right
singular vectors. These vectors can be thought of as the projection of
the protein conformations onto a lower dimensional basis defined by
the left singular vectors.

The elements of the right singular vector can be thought of as
scaling the size of the left singular vector to describe where the
atom is at each time-point or in each conformation.
The right singular vectors are what are used to classify each
structure for identifying conformational substates.