Question: Find the Jacobian matrix of the differentiable function, $ f : \mathbb{R}^n \to \mathbb{R} $ defined by $ f(x) = \langle Ax, x \rangle $, where $ A : \mathbb{R}^n \to \mathbb{R}^n $ is a linear transformation.
My approach:
I computed the derivative linear map from $\mathbb{R}^n \to \mathbb{R}$ denoted by $df_x(h)$ = $\langle Ax, h \rangle$ + $\langle Ah, x \rangle$
but i am not able to proceed from here on how to calculate the jacobian matrix. i am having trouble on getting the matrix of this linear transformation with respect to the standard basis.