\begin{definition}[Definition:Left Null Space]
Let $R$ be a ring.
Let $\mathbf A$ be a matrix in the matrix space $\map {\MM_{m, n} } R$.
Let $\mathbf A^\intercal$ be the transpose of $\mathbf A$.
The '''left null space''' '''$\mathbf A$''' is defined as the null space of $\mathbf A^\intercal$.
\end{definition}