\begin{definition}[Definition:Row Space]
Let $R$ be a ring.
Let $\mathbf A$ be a matrix over $R$.
Let $\mathbf A^\intercal$ be the transpose of $\mathbf A$.
 
Let the columns of $\mathbf A^\intercal$ be members of a vector space.
The '''row space of $\mathbf A$''' is defined as the column space of $\mathbf A^\intercal$.
\end{definition}