From solving a hard-margin SVM primal problem we get: $$ w = \sum{\alpha_i y_i x_i} \\ \sum{a_i y_i} = 0 $$
Where $\alpha$ is the lagrangian multiplier vector. After solving for $w$ (using the dual problem) we can also solve for $b$ (the bias) with one of the support vectors by $$y_i(wx_i+b)=1$$
Given that, I'm looking for a way to prove that $$\lVert w \rVert ^2 = \sum{\alpha_i}$$
Thanks.