Definition:Invariant Metric on Vector Space

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Definition

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 $x, y, z \in X$.


Sources