Definition:Linear Combination of Subsets of Vector Space/Dilation

Definition
Let $K$ be a field.

Let $X$ be a vector space over $K$. Let $E$ be a subset of $X$ and let $\lambda \in K$.

We define the dilation of $E$ by $\lambda$, written $\lambda E$, by:


 * $\lambda E = \set {\lambda x : x \in E}$