Volumes of n-dimensional parallelepipeds in lp spaces
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Date
2016-02-17
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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.
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Keywords
n-dimensional parallelepipeds, semi-inner products, rthogonal projection in normed spaces, n-norms, lp spaces