What is the correct answer of $\cfrac{\partial Ax}{\partial x}$, where $A \in \mathbb{R}^{m \times n}$ and $x \in \mathbb{R}^{n}$(column vector).
Here in page 2, the answer is $$\nabla_{x} A x=\left[\begin{array}{c}{\nabla_{x} \tilde{a}_{1}^{T} x} \\ {\nabla_{x} \tilde{a}_{2}^{T} x} \\ {\vdots} \\ {\nabla_{x} \tilde{a}_{m}^{T} x}\end{array}\right]=\left[\begin{array}{cccc}{\tilde{a}_{1}} & {\tilde{a}_{2}} & {\cdots} & {\tilde{a}_{m}}\end{array}\right]=A^{T}$$
While here in page 3, the answer is
$A$.
For me, I think the correct answer should be $A$. Is it right?
2026-03-25 20:20:17.1774470017
Given matrix $A$ and column vector $x$, what is the derivative of $Ax$ with respect to $x$?
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