Wedge product/Parallelotopes/Remark

It is not easy to build up an imagination for the expressions $v_{1} \land \dots \land v_{n}$ and $\land$ . More important than the "meaning“ of these symbols is their transformation behavior and the calculation rules. It is rather the working with these symbols that gives them their meaning. However, we can say in a vague sense that $v_{1} \land \dots \land v_{n}$ represents the "oriented“ parallelotope generated by the vectors $v_{1}, \dots, v_{n}$ . The wedge product $\overset{n}{⋀} V$ consists of all linear combinations of such parallelotopes.