Affine-Invariant Midrange Statistics
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We formulate and discuss the affine-invariant matrix midrange problem on the cone of n× n positive definite Hermitian matrices ℙ(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.
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