dual space

Noun

Meaning

(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.

Source: en.wiktionary.org

Synonyms

continuous dual algebraic dual space dual vector space continuous dual space

Examples

A Banach space can be canonically identified with a subspace of its bidual, which is the dual of its dual space. Source: Internet

Example: dual of a finite-dimensional vector space Every finite-dimensional vector space is isomorphic to its dual space, but there may be many different isomorphisms between the two spaces. Source: Internet

For example, the canonical map from a finite-dimensional vector space V to its second dual space is a canonical isomorphism; on the other hand, V is isomorphic to its dual space but not canonically in general. Source: Internet

In Banach spaces, a large part of the study involves the dual space : the space of all continuous linear maps from the space into its underlying field, so-called functionals. Source: Internet

In that approach a type (p, q) tensor T is defined as a map, : where V is a (finite-dimensional) vector space and V* is the corresponding dual space of covectors, which is linear in each of its arguments. Source: Internet

In the dual space, it expresses the creation of the economic values associated with the outputs from set input unit prices. Source: Internet

Close letter words and terms

dual school dual shotgun dual sounds dual star dual stars dual suite