Category:Invariant Metrics on Vector Spaces

This category contains results about Invariant Metrics on Vector Spaces.
Definitions specific to this category can be found in Definitions/Invariant Metrics on Vector Spaces.

Let $K$ be a field.

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

Let $d$ be a metric on $X$.

We say that $d$ is invariant if and only if:

$\map d {x, y} = \map d {x + z, y + z}$

for each $x, y, z \in X$.