Affine-Invariant Midrange Statistics

We formulate and discuss the affine-invariant matrix midrange problem on the cone of n× n positive definite Hermitian matrices mathbbP(n), which is based on the Thompson metric. A particular computationally efficient midpoint of this metric is investigated as a highly scalable candidate for an average of two positive definite matrices within this context, before studying the N-point problem in the vector and matrix settings.