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 $x, y, z \in X$.
Also see
- Results about invariant metrics on vector spaces can be found here.
Sources
- 1991: Walter Rudin: Functional Analysis (2nd ed.) ... (previous) ... (next): $1.7$: Invariance