$\| \cdot \|_p, p = \frac{1}{2}$ or "half norm" is not a norm
What is a quick way to verify that it is indeed not a norm?
2026-04-18 08:21:04.1776500464
Can someone explain why $\| \cdot \|_p, p = \frac{1}{2}$ isn't a norm?
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The Ball of unity that is induced by the "norm" is not convex. The points $(1, 0)$ and $(0, 1)$ are in the Ball, but their midpoint isn't.
This can be visualized in this plot.