 Since this is an orthogonal decomposition, Pythagorean theorem says formula_36, and taking expectations we get formula_37, as above (but times formula_38).If the distribution of formula_39 is rotationally symmetric, as in the case when formula_40 are sampled from a Gaussian, then on average, the dimension along formula_34 contributes to formula_42 equally as the formula_43 directions perpendicular to formula_34, so that formula_45 and formula_46.This is in fact true in general, as explained above.