Изменения

<tex> F^+ = (U D V^T V D U^T)^{-1} U D V^T = U D^{-1} V^T = \sum\limits_{j=1}^n \frac{ 1 }{ \sqrt{ \lambda_j } } u_j v_j </tex>; <tex> \alpha^* = F^+ y = U D^{-1} V^T y = \sum\limits_{j=1}^n \frac{ 1 }{ \sqrt{ \lambda_j } } u_j (v_j^T y) </tex>; <tex> F \alpha^* = P_F y = (V D U^T) U D^{-1} V^T y = V V^T y = \sum\limits_{j=1}^n v_j (v_j^T y) </tex>; <tex> || \alpha^* ||^2 = ||D^{-1} V^T y||^2 = \sum\limits_{j=1}^n \frac{ 1 }{ \lambda_j } (v_j^T y)^2 </tex>.