Abstract:
Given a linearly independent set of n vectors in a normed space, we are
interested in computing the “volume” of the n-dimensional parallelepiped
spanned by them. In `p (1 p < 1), we can use the known semi-inner
product and obtain, in general, n! ways of doing it, depending on the order
of the vectors. We show, however, that all resulting “volumes” satisfy one
common inequality.
