A primer on Vector Calculus. trace constituents for square A \in \mathbb{R}^{m\times m}, we write: requirements \text{tr}\left(A\right) = \sum_{i}^{} A_{ii} is the sum of the diagonals additional information properties of traces \begin{equation} \text{tr}\left(AB\right) = \text{tr}\left(BA\right) \end{equation}
\begin{equation} \text{tr}\left(ABC\right) = \text{tr}\left(CAB\right) \end{equation}
\begin{equation} \nabla_{A} \left[\text{tr}\left(AB\right)\right] = B^{T} \end{equation}