Definition:Translation of Subset of Vector Space
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Definition
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.