  One of the main challenges for ab initio nuclear many-body theory is the
growth of computational and storage costs as calculations are extended to
heavy, exotic, and structurally complex nuclei. Here, we investigate the
factorization of nuclear interactions as a means to address this issue. We
perform Singular Value Decompositions of nucleon-nucleon interactions in
partial wave representation and study the dependence of the singular value
spectrum on interaction characteristics like regularization scheme and
resolution scales.
  We develop and implement the Similarity Renormalization Group (SRG) evolution
of the factorized interaction, and demonstrate that this SVD-SRG approach
accurately preserves two-nucleon observables.
  We find that low-resolution interactions allow the truncation of the SVD at
low rank, and that a small number of relevant components is sufficient to
capture the nuclear interaction and perform an accurate SRG evolution, while
the Coulomb interaction requires special consideration. The rank is uniform
across all partial waves, and almost independent of the basis choice in the
tested cases. This suggests an interpretation of the relevant singular
components as mere representations of a small set of abstract operators that
can describe the interaction and its SRG flow.
  Following the traditional workflow for nuclear interactions, we discuss how
the transformation between the center-of-mass and laboratory frames creates
redundant copies of the partial wave components when implemented in matrix
representation, and we discuss strategies for mitigation.
  Finally, we test the low-rank approximation to the SRG-evolved interactions
in many-body calculations using the In-Medium SRG. By including nuclear radii
in our analysis, we verify that the implementation of the SRG using the
singular vectors of the interaction does not spoil the evolution of other
observables.
