双重空间

Basic Analysis III Pub Date : 2020-07-19 DOI:10.1201/9781315166209-13

J. Peterson

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摘要

定义1(对偶空间)设V是一个有限维向量空间。(a) V上的线性泛函是一个函数u *: V→IR，它是线性的，因为对于所有u, w∈V和所有α∈IR, u * (V + w) = u * (V) + u * (w)和u * (α V) = α u * (V)。

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Dual Spaces

Definition 1 (Dual Space) Let V be a finite dimensional vector space. (a) A linear functional on V is a function u * : V → IR that is linear in the sense that u * (v + w) = u * (v) + u * (w) and u * (α v) = α u * (v) for all u, w ∈ V and all α ∈ IR.

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Basic Analysis III

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