  Given $n+1$ unit vectors in $\mathbf{R}^n$ or $\mathbf{C}^n,$ consider the
absolute values of the determinants of the vectors taken $n$ at a time. By
taking a geometric perspective, we show that the minimum of these determinants
is maximized when the vectors point from the origin to the vertices of a
regular simplex inscribed in the unit sphere in $\mathbf{R}^n,$ even in the
complex case. We also discuss variations on this problem and a few connections
to other problems.
