Definition:Translation Mapping/Vector Space

Definition

Let $K$ be a field.

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

Let $x \in X$.

We define the translation mapping $\tau_x : X \to X$ by:

$\map {\tau_x} y = y - x$

for each $y \in X$.

Also known as

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

Sources

• 1991: Walter Rudin: Functional Analysis (2nd ed.) ... (previous) ... (next): $1.6$: Topological vector spaces