Rookie question; for a vector space ##V##, with basis ##v_1, v_2, \dots, v_n##, the dual space ##V^*## is the set of linear functionals ##\varphi: V \rightarrow \mathbb{R}##. Dual basis will satisfy ##\varphi^i(v_j) = \delta_{ij}##. Is the action of any dual vector on any vector always an inner...