  The singular value decomposition (SVD) is a popular matrix factorization that
has been used widely in applications ever since an efficient algorithm for its
computation was developed in the 1970s. In recent years, the SVD has become
even more prominent due to a surge in applications and increased computational
memory and speed.
  To illustrate the vitality of the SVD in data analysis, we highlight three of
its lesser-known yet fascinating applications: the SVD can be used to
characterize political positions of Congressmen, measure the growth rate of
crystals in igneous rock, and examine entanglement in quantum computation. We
also discuss higher-dimensional generalizations of the SVD, which have become
increasingly crucial with the newfound wealth of multidimensional data and have
launched new research initiatives in both theoretical and applied mathematics.
With its bountiful theory and applications, the SVD is truly extraordinary.
