to Remark 6, we can consider in R p × q × R q × q the topology induced by the norm Given ( B$_{0}$ , Σ$_{0}$ ) in R p × q × R q × $^{q}$, the proof consists in find an upper bound of | d $^{2}$( B , Σ ) − d $^{2}$( B$_{0}$ , Σ$_{0}$ ) | that tends to 0 when ‖| ( B , Σ ) − ( B$_{0}$ , Σ$_{0}$ ) ‖| → 0 . Adding and subtracting d $^{2}$( B$_{0}$ , Σ ) we have that Let r ( B$_{0}$ ) = ( y − B ′ $_{0}$x ). Using basic tools from linear algebra we obtain and by Weyl’s Perturbation Theorem (see [4], pg. 63), we have that combining these inequalities we obtain a bound of | d $^{2}$( B , Σ ) − d $^{2}$( B$_{0}$ , Σ ) | that tends to 0 when ‖| ( B , Σ ) − ( B$_{0}$ , Σ$_{0}$ ) ‖| → 0 . If r ( B$_{0}$ ) = 0 the lemma is proved, otherwise using the Cauchy-Schwarz in- equality and (A.6) we have which completes the proof. ■ Proof of Theorem 1: By Lemma 9, it sufices to show that there exist t$_{1}$ and t$_{2}$ 30 ∣ d $^{2}$( B$_{0}$ , Σ ) − d $^{2}$( B$_{0}$ , Σ$_{0}$ ) ∣ ≤ ‖ Σ − 1 0 ‖‖ r ( B$_{0}$ ) ‖ $^{2}$‖ | ( B , Σ ) − ( B$_{0}$ , Σ$_{0}$ ) ‖| λ$_{q}$ ( Σ$_{0}$ ) − ‖| ( B , Σ ) − ( B$_{0}$ , Σ$_{0}$ ) ‖| , λ$_{1}$ ( Σ − $^{1}$) = 1 λ$_{q}$ ( Σ ) < 1 λ$_{q}$ ( Σ$_{0}$ ) − ‖| ( B , Σ ) − ( B$_{0}$ , Σ$_{0}$ ) ‖| , (A.6) ∣ d $^{2}$( B , Σ ) − d $^{2}$( B$_{0}$ , Σ ) ∣ ≤ q ‖| ( B , Σ ) − ( B$_{0}$ , Σ$_{0}$ ) ‖| ( ‖ x ‖ + 2 ‖ r ( B$_{0}$ ) ‖ ) ‖ x ‖ λ$_{1}$ ( Σ − $^{1}$) , ∣ d $^{2}$( B , Σ ) − d $^{2}$( B$_{0}$ , Σ$_{0}$ ) ∣ ≤ ∣ d $^{2}$( B , Σ ) − d $^{2}$( B$_{0}$ , Σ ) ∣ + ∣ d $^{2}$( B$_{0}$ , Σ ) − d $^{2}$( B$_{0}$ , Σ$_{0}$ ) ∣ . ‖| ( A , V ) ‖| = sup {‖ A ‖ $_{2}$, ‖ V ‖} . (A.5)