\begin{definition}[Definition:Direct Product of Vector Spaces/General Case]
Let $K$ be a field.
Let $\family {V_i, +_i, \circ_i}_{i \mathop \in I}$ be a family of $K$-vector spaces.
The '''(external) direct product''' of $\family {V_i, +_i, \circ_i}_{i \mathop \in I}$ is their module direct product.
Category:Definitions/Examples of Vector Spaces
Category:Definitions/Direct Products
\end{definition}