For matrices $A,B\in\mathbb F^{m\times n}$, their sum is defined entrywise: $(A+B)_{ij}=a_{ij}+b_{ij}$. The shapes must agree. For example, $\begin{bmatrix}1&2\\3&4\end{bmatrix}+\begin{bmatrix}5&0\\-1&2\end{bmatrix}=\begin{bmatrix}6&2\\2&6\end{bmatrix}$. Matrix addition represents addition of linear maps with the same domain and codomain.
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