dual space
Noun
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Noun
dual space (plural dual spaces)
- (mathematics) The vector space which comprises the set of linear functionals of a given vector space.
- (mathematics) The vector space which comprises the set of continuous linear functionals of a given topological vector space.
- 2011, David E. Stewart, Dynamics with Inequalities, Society for Industrial and Applied Mathematics, page 17 ↗,
- The dual space of a Banach space X is the vector space of continuous linear functions X \rightarrow\mathbb{R}, which are called functionals. Similar notation is used for duality pairing between the Banach space X and its dual space X': \left\langle u, v\right\rangle is the result of applying the functional u \in X' to v \in X: \left\langle u, v\right\rangle = u(v) explicitly uses the fact that u is a function X \rightarrow\mathbb{R}.
- 2011, David E. Stewart, Dynamics with Inequalities, Society for Industrial and Applied Mathematics, page 17 ↗,
- (vector space of linear functionals) algebraic dual space, dual vector space
- (vector space of continuous linear functionals) continuous dual space, continuous dual
This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.002