dual space

== English == === 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. ==== Usage notes ==== 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 ==== (vector space of linear functionals): algebraic dual space, dual vector space (vector space of continuous linear functionals): continuous dual space, continuous dual === Further reading === Linear form on Wikipedia.Wikipedia