Given a function $f:\Delta^n \to Y$ from a simplex into a riemmannian manifold. Furthermore given a point $x \in \Delta^n$ we can send an orthonormal basis at $x$ using $D_x f$ to a set of vectors defining a parallelepiped. I know that the volume of a parallelepiped can be calculated using the absolute value of the determinant of its defining vectors.
So it would be convenient to write $\left|\det(D_x f)\right|$. But the Jacobian $D_x f$ is not necessarily a square matrix.
Is there a notational way to fix this?
EDIT: What I am looking for is a simple notation to write this down.