  Covariance matrix estimation is a persistent challenge for cosmology, often
requiring a large number of synthetic mock catalogues. The off-diagonal
components of the covariance matrix also make it difficult to show
representative error bars on the 2-point correlation function (2PCF), since
errors computed from the diagonal values of the covariance matrix greatly
underestimate the uncertainties. We develop a routine for decorrelating the
projected and anisotropic 2PCF with simple and scale-compact transformations on
the 2PCF. These transformation matrices are modeled after the Cholesky
decomposition and the symmetric square root of the Fisher matrix. Using mock
catalogues, we show that the transformed projected and anisotropic 2PCF recover
the same structure as the original 2PCF, while producing largely decorrelated
error bars. Specifically, we propose simple Cholesky based transformation
matrices that suppress the off-diagonal covariances on the projected 2PCF by
~95% and that on the anisotropic 2PCF by ~87%. These transformations also serve
as highly regularized models of the Fisher matrix, compressing the degrees of
freedom so that one can fit for the Fisher matrix with a much smaller number of
mocks.
