Definition:Translation of Subset of Vector Space

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Let $K$ be a field.

Let $X$ be a vector space over $K$.

Let $E$ be a subset of $X$.

Let $x \in X$.

We define the translation of $E$ by $x$ as the set:

$E + x = \set {u + x : u \in E}$

Also see

  • Results about translation of subsets of vector spaces can be found here.