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arXiv · 2607.27714

Mostow-Type Decompositions and Geometric Means for Symmetric Cones

Khalid Koufany·Yongdo Lim
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Abstract

Motivated by Mostow's decomposition theorem for positive definite matrices and by subsequent matrix factorizations involving geometric means, we establish a Mostow-type decomposition for arbitrary symmetric cones. As a consequence, we derive an analogous decomposition for the automorphism group of the cone. We also introduce a natural Hadamard metric on the symmetric cone by pulling back an $\ell^2$-product metric, together with its midpoint operation and associated Karcher mean.

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Khalid Koufany, Yongdo Lim. 2026-07-30. Mostow-Type Decompositions and Geometric Means for Symmetric Cones. https://arxiv.org/abs/2607.27714

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