Considering a distance d(x,y) = $d_A(x,y)$ defined in form: $\|x-y\|_A = \sqrt{(x-y)^TA(x-y)}$ where A is matrix (positive semi-definite).
Let $f=\|x-y\|_A$, so i want to calculate $\dfrac{\partial f}{\partial A}$
Idea is to minimize function by gradient method so partial derivation is needed. What would be the answer? Thanks.