Given a finite-dimensional vector space \({V}\), the dual space \({V^{*}}\) is defined to be the set of linear mappings from \({V}\) to the scalars (AKA the linear functionals on \({V}\)). The elements of \({V^{*}}\) can be added together and multiplied by scalars, so \({V^{*}}\) is also a vector space, with the same dimension as \({V}\).
Δ Note that in general, the word “dual” is used for many concepts in mathematics; in particular, the dual space has no relation to the Hodge dual. |