  A fundamental assumption in cosmology is that of statistical isotropy - that
the universe, on average, looks the same in every direction in the sky.
Statistical isotropy has recently been tested stringently using Cosmic
Microwave Background (CMB) data, leading to intriguing results on large angular
scales. Here we apply some of the same techniques used in the CMB to the
distribution of galaxies on the sky. Using the multipole vector approach, where
each multipole in the harmonic decomposition of galaxy density field is
described by unit vectors and an amplitude, we lay out the basic formalism of
how to reconstruct the multipole vectors and their statistics out of galaxy
survey catalogs. We apply the algorithm to synthetic galaxy maps, and study the
sensitivity of the multipole vector reconstruction accuracy to the density,
depth, sky coverage, and pixelization of galaxy catalog maps.
