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 $X$.

Let $\lambda \in K$.

The dilation of $E$ by $\lambda$ is defined and written as:


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

where $\lambda x$ is the scalar product of $x$ by $\lambda$.