Dual Vector Spaces

Definition

The dual vector space (or dual space, algebraic dual space) of a vector space $V$ over a field $\F $ is the space $\mathcal{L} (V, \F )$. In other words, the dual space is the set of linear functionals on $V$.

Notation

There are many notations in use. We will use $V'$. Another common notation is $V^*$ (however we reserve this notation for adjoints, to come).