Then, perhaps the main statistical implication of the result is that not only can we decompose the combined variances of all the elements of into decreasing contributions due to each PC, but we can also decompose the whole covariance matrix into contributions formula_56 from each PC. Although not strictly decreasing, the elements of formula_56 will tend to become smaller as formula_58 increases, as formula_56 is nonincreasing for increasing formula_58, whereas the elements of formula_61 tend to stay about the same size because of the normalization constraints: formula_62.