Homogeneous and isotropic correlations
Matrix form of the covariances: B = S C S
where S is a diagonal matrix containing the standard deviations.
Homogeneous and isotropic correlation models
C(x1,x2) = f(|x1 - x2|)
Isotropic: function depends only on the distance between two points
Homogeneous: this dependency is the same everywhere (the correlation function does not change)
Homogeneous and isotropic correlations do not imply that the covariances have also this property since the standard deviations can vary from one point to the other
Spectral form of homogeneous and isotropic correlations is a diagonal matrix.