to the signal part of the correlation matrix, $S_{ij}$. The second term corresponds to the shot noise. When the cells do not overlap, the matrix $K_{ij}$ is diagonal: $$K_{ij} =
   \frac{\delta_{ij}}{V_i} 
   \int d^3s
   {K_i}^2({{\mbox{\boldmath $s$}}}), \qquad \mbox{(non-overlapping)},
\label{eq2-9-3}$$ (no sum over $i$, $j$), where $\delta_{ij}$ is the Kronecker’s delta. For the non-overlapping top-hat kernel, this equation is simplified as $K_{ij} = \delta_{ij}$, and the correlation matrix is simply given by $$R_{ij} = N_i N_j \xi^{\rm (s)}_{ij} +
   N_i \delta_{ij} + E_{ij}, \qquad (\mbox{non-overlapping,\ top-hat})
\label{eq2-9-4}$$ (no sum over $i$, $j$).

Unlike the correlation function in real space, the correlation function in redshift space is neither isotropic nor homogeneous. The correlation function in real space is a function of separations between two-points, $\xi(|{{\mbox{\boldmath $x$}}}_1 - {{\mbox{\boldmath $x$}}}_2|)$. However, the redshift space is distorted from the real space, and consequently the correlation function is no longer the function of the separation only.

The comoving distance to a galaxy is not a primary observable quantity and the redshift is the only estimate of the real distance from the Earth to the cosmologically distant galaxies. Since the redshift is not identical to the comoving distance, the redshift space is anisotropically distorted from the real 