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:

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

Sources

• 1990: John B. Conway: A Course in Functional Analysis (2nd ed.) ... (previous) ... (next): Appendix $\text{A}$ Preliminaries: $\S 1.$ Linear Algebra