\begin{definition}[Definition:Dimension (Representation Theory)]
Let $\struct {k, +, \circ}$ be a field.
Let $V$ be a vector space over $k$ of finite dimension.
Let $\GL V$ be the general linear group of $V$.
Let $\struct {G, \cdot}$ be a finite group.
Let $\rho: G \to \GL V$ be a linear representation of $G$ on $V$.
The '''dimension''' or '''degree''' of $\rho$, written $\map \deg \rho$ is the dimension of the vector space $V$.
Category:Definitions/Representation Theory
\end{definition}