Last Updated
：2025/11/20
semi-norm
Noun
Japanese Meaning
半ノルム: 数学解析における概念で、ベクトル v に対して非負の実数を割り当てる写像です。具体的には、任意のスカラー c について ∥cv∥ = |c|∥v∥ の性質と、三角不等式 ∥v + w∥ ≤ ∥v∥ + ∥w∥ を満たします。ただし、∥v∥ = 0 が必ずしも v = 0 を意味しないため、通常のノルムとの差異があります。
Sense（1）
（ plural ）
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(mathematical analysis) A function denoted ∥v∥ that maps a vector v to a non-negative value such that ∥cv∥ = |c|.∥v∥, where c is a scalar, and ∥v + w∥ ≤ ∥v∥ + ∥w∥ (the triangle inequality); the condition that ∥v∥ = 0 implies that v = 0 is not required, but when it holds, the semi-norm is a norm.
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semi-norm
To prove convergence, she introduced a semi-norm on the space of functions that vanishes on a subspace while still satisfying positive homogeneity and the triangle inequality.
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To prove convergence, she introduced a semi-norm on the space of functions that vanishes on a subspace while still satisfying positive homogeneity and the triangle inequality.
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