Could someone please help me prove that every metric on a linear space is induced by norm if and only if the metric is homogeneous and translation invariant? I found this answer about homogeneity but I'm not sure how to extend this to every metric. Thank you.
2026-02-22 18:17:19.1771784239
Metric on a linear space is induced by norm if and only if the metric is homogeneous and translation invariant
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