$\alpha$ is a scalar, $W$ is a matrix, s and h are vectors, I is identity matrix. I know the derivative is as follows: $\frac { \partial J(s) }{ \partial s } =2(I-\alpha W)s+2(1-\alpha )h\quad$
but I am wondering about the steps. I don't get the above results according to the hints in matrix cookbook. Anybody can help me?
Denoting the scalar product in a more legible form we have $$\begin{align} D_vJ(s)&=D_v(\alpha\langle s,(I-W)s\rangle+(1-\alpha)\|s-h\|^2\\ &=\alpha\bigl(\langle v,(I-W)s\rangle+\langle s,(I-W)v\rangle\bigr)+\\ &\quad +2(1-\alpha)\langle s-h,v\rangle\\ &=\alpha\bigl(\langle v,s\rangle-\langle v,Ws\rangle +\langle s,v\rangle-\langle s,Wv\rangle\bigr)+\\ &\quad+2\langle s,v\rangle-2\alpha\langle s,v\rangle +2(1-\alpha)\langle h,v\rangle\\ &=2\langle s,v-\alpha Wv\rangle +2(1-\alpha)\langle h,v\rangle\\ &=2\langle (I-\alpha W)s+(1-\alpha)h,v\rangle \end{align},$$ that is $$\nabla J(s)=2(I-\alpha W)s+2(1-\alpha)h$$ as claimed.