Question

Finite-dimensional linear spaces. A particular feature in this case is that the (algebraic) dual of a finite-dimensional vector space, namely the space of linear maps from the vector space into the base field, is isomorphic to the original space (since it is of the same dimensionality) but not canonically so. In contrast, the bi-dual (the dual of the dual) is canonically isomorphic to the original space, and so may be identified with it.