I'm having trouble understanding why the $x'$ vector, that is the projection of the $x$ vector on the $w_1$ axis, is equivalent to $x'=w_1( w^T_1 x )$. Shouldn't $x'$ be equivalent to the dot product of the versor of the $w_1$ and the $x$ vector multiplied by the versor of the $w_1$ axis?
