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and in the limit, for large v (where P(')(v) has converged to VaV H ) we can write,
r+2
dP('ig)(r) = ~ Pi(P(80)(r)RPi(r)+ Pi(r)RP('ig)(r)) (25)
dr
i=r+l
This ODE shares the same convergence properties as (15). Since the signal subspace
converges to the dominant r-dimensional subspace of it, and the sphericalized component
of the signal subspace converges to the dominant (r - 1)-dimensional subspace of R, we
have that vr(r)~vr 9 Another similar induction step shows that Vr+I(V)--*Vr+I and thus
the orthogonal complement satisfies P(n)(r)~P('0 .
Theorem 2. The four ...