AI 中文总结
该研究为任意对称锥建立Mostow型分解，推导其自同构群的类似分解，引入对称锥上的Hadamard度量及其中点运算与Karcher均值，丰富了对称锥的几何分析理论。
AI 中文摘要
受正定矩阵的Mostow分解定理及后续涉及几何平均的矩阵分解启发，我们为任意对称锥建立了Mostow型分解。作为结果，我们推导出该锥自同构群的类似分解。我们还通过拉回ℓ²乘积度量，在对称锥上引入自然的Hadamard度量，以及其中点运算和相关的Karcher均值。
英文摘要
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.
