# Tensor algebras on the dual space

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.