(1) β 1 = α 1 \beta_1=\alpha_1 β1​=α1​ (2) β j = α j − ( β 1 , α j ) ( β 1 , β 1 ) β 1 − ( β 2 , α j ) ( β 2 , β 2 ) β 2 − ( β j − 1 , α j ) ( β j − 1 , β j − 1 ) β j − 1 \beta_j=\alpha_j-\frac{(\beta_1,\alpha_j)}{(\beta_1,\beta_1)}\beta_1-\frac{(\beta_2,\alpha_j)}{(\beta_2,\beta_2)}\beta_2-\frac{(\beta_{j-1},\alpha_j)}{(\beta_{j-1},\beta_{j-1})}\beta_{j-1} βj​=αj​−(β1​,β1​)(β1​,αj​)​β1​−(β2​,β2​)(β2​,αj​)​β2​−(βj−1​,βj−1​)(βj−1​,αj​)​βj−1​ (3) η j = β j ∣ ∣ β j ∣ ∣ , j = 1 , 2 , . . . , m \eta_j=\frac{\beta_j}{||\beta_j||},j=1,2,...,m ηj​=∣∣βj​∣∣βj​​,j=1,2,...,m