dual space
English[edit]
Noun[edit]
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 is the vector space of continuous linear functions , which are called functionals. Similar notation is used for duality pairing between the Banach space and its dual space : is the result of applying the functional to : explicitly uses the fact that is a function .
- 2011, David E. Stewart, Dynamics with Inequalities, Society for Industrial and Applied Mathematics, page 17,
Usage notes[edit]
Defined for all vector spaces, the dual space may, for clarity, be called the algebraic dual space. When defined for a topological vector space, the (algebraic) dual space has a subspace that corresponds to continuous linear functionals and is called the continuous dual space or continuous dual — or simply the dual space.
Synonyms[edit]
- (vector space of linear functionals): algebraic dual space, dual vector space
- (vector space of continuous linear functionals): continuous dual space, continuous dual
Further reading[edit]
- Linear form on Wikipedia.Wikipedia