Gram determinant
= Gram determinant
{c}
{title2=$\det(\langle v_i,v_j\rangle)_{i,j}$}
The determinant of a <Gram matrix> is nonnegative and vanishes precisely when its vectors are <linearly dependent>. In Euclidean three-dimensional space, three column vectors form a square <matrix> $V$, whose <Gram matrix> is $V^TV$. Its determinant is $(\det V)^2=[v_1\cdot(v_2\times v_3)]^2$, the square of the <scalar triple product> and of the parallelepiped volume.