I was reading my adaptive control textbook, and I noticed that my professor used a notation that is somehow confusing me.
$$J\left(\Theta\right) = \frac{1}{2}\epsilon^T\epsilon$$ where $\Theta \in \mathbb{R}^{m\times n}$, and $\epsilon \in \mathbb{R}^n \rightarrow J\in \mathbb{R}$. When taking the derivative of the scalar with respect to the matrix $\Theta$, he writes it as
$$\frac{\partial J^T}{\partial\Theta^T}$$ instead of $$\frac{\partial J}{\partial\Theta}$$
Can someone explain the meaning of the former notation of the derivative?