What is the "cross product" of $n-1$ vectors in $\mathbb{R}^n$ called?

Question

Is there a name for the following determinant ($v_1, ... v_{n-1}$ are vectors in $\mathbb{R}^n$)?

$$\det\begin{pmatrix} \mathbf{e_1}&\cdots&\mathbf{e_n}\\ (v_1)_1&\cdots&(v_1)_n\\ \vdots&\ddots&\vdots\\ (v_{n-1})_1&\cdots&(v_{n-1})_n\\ \end{pmatrix}$$