ScalingStacks

Lemma 2.13 . [00HH]

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Lemma 2.13.

Let (V,∥⋅∥)(V,\lVert\mathord{\cdot}\rVert) be a finite-dimensional ultrametrically normed vector space over kk. If {vi}i∈{1,…,n}\{v_{i}\}_{i\in\{1,\dots,n\}} is a finite set of elements of VV such that {∥vi∥}i∈{1,…,n}\{\lVert v_{i}\rVert\}_{i\in\{1,\dots,n\}} are disctinct in ℝ+\mathbb{R}_{+}. Then ∥∑i∈{1,…,n}vi∥=maxi∈{1,…,n}⁡∥vi∥\lVert\sum_{i\in\{1,\dots,n\}}v_{i}\rVert=\max_{i\in\{1,\dots,n\}}\lVert v_{i}\rVert.

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