Going from matrix form to summation for calculating the derivative

Question

I have troubles calculating the derivatives of: $\frac{dy}{dx}$ if $y= \vec{x}^{T}\matrix{W}\vec{x}$

I think it would be easier if I go to summation form and then take it from there. However, i'm not sure on how to do that? Same thing when I have a summation to go back to matrix form. Is there an easy step by step guide for this?

Answer 1

Hint:

Let $\mathbf{A}$ be a matrix of size $n \times m$ with elements $A_{ik}$ for $i = 1, 2 \dots, n$ and $k = 1, 2, \dots, m$

Let $\mathbf{B}$ be a matrix of size $m \times p$ with elements $B_{kj}$ for $k = 1, 2 \dots, m$ and $j = 1, 2, \dots, p$

Then, we have \begin{align} (\mathbf{A} \, \mathbf{B})_{ij} \; = \; \sum_{k=1}^{m}A_{ik} \, B_{kj} \end{align}