Category:Dilation of Subsets of Vector Spaces

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This category contains results about Dilation of Subsets of Vector Spaces.
Definitions specific to this category can be found in Definitions/Dilation of Subsets of Vector Spaces.

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 $\lambda$.