\begin{definition}[Definition:Antisymmetric Matrix]
Let $R$ be a ring.
Let $\mathbf A$ be a square matrix over $R$.
$\mathbf A$ is '''antisymmetric''' {{iff}}:
:$\mathbf A = - \mathbf A^\intercal$
where $\mathbf A^\intercal$ is the transpose of $\mathbf A$.
\end{definition}