A D403: Square matrix $x : J \times J \to X$ is symmetric if and only if $$\begin{equation} \forall \, i, j \in J : x_{i, j} = x_{j, i} \end{equation}$$

A D403: Square matrix $x : J \times J \to X$ is symmetric if and only if $$\begin{equation} x = x^T \end{equation}$$