Definition:Translation Mapping/Vector Space

Definition
Let $K$ be a field.

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

Let $x \in X$.

The translation mapping $\tau_x : X \to X$ is defined as:


 * $\forall y \in X: \map {\tau_x} y = y - x$

where $y - x$ denotes vector subtraction.

Euclidean Space
This is often defined separately when the vector space in question is a Euclidean space:

Also known as
The map $\tau_x$ may also be called the translation (by $x$) operator.