is discussed in §3.4. Fast methods to compute the linear correlation matrix in projected 2-dimensional samples are provided in §3.5. In §4 additional techniques in applying the present methods to the KL eigenmodes are explained. Finally, the presented methods are summarized and discussed in §5.

 The Eigenmode Analysis and Importance of the Correlation Matrix \[sec2\] 
==========================================================================

In this section we briefly review the eigenmode analysis originally introduced by @vog96 in the context of the redshift surveys. The importance of accurately modeling the correlation matrix in redshift space and of developing a numerically fast algorithm to calculate the model matrices, which are the main subject of this work, will be clarified in this section.

Bayesian Analyses of the Huge Data Sets \[sec2-1\]
--------------------------------------------------

One of the central motivation of the eigenmode analysis comes from the difficulty in direct Bayesian analysis of huge data sets of observed galaxy distributions. It is desirable that the cosmological models are discriminated by the galaxy distribution itself, not relying on the inverse problem of determining the underlying density power spectrum from observed galaxy distributions. While a cosmological model predicts the linear power spectrum, the dependence of the galaxy clustering in redshift surveys on the theoretical power 