Translate Sets

Definition

The translate of a subset of a vector space by a given vector is the set of all vectors which are the sum of a vector in the subset with the given vector.

Notation

Let $(V, \F )$ be a vector space. Let $M \subset V$ and $a \in V$. The translate of $M$ by $a$ is the set

\[ \Set*{x + a}{x \in M}, \]