Definition:Zero Mapping/Vector Space
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Definition
Let $Y$ be a vector space.
Let $S$ be a set.
Let $\mathbf 0_Y$ be the identity element of $Y$.
Suppose $\mathbf 0 : S \to Y$ is a mapping such that:
- $\forall x \in S: \map {\mathbf 0} x = \mathbf 0_Y$
Then $\mathbf 0$ is referred to as the zero mapping.
Sources
- 2017: Amol Sasane: A Friendly Approach to Functional Analysis ... (previous) ... (next): Chapter $\S 2.1$: Continuous and linear maps. Linear transformations