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On Jordan angles and triangle inequality in Grassmannian

Yurii A. Neretin
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Abstract

We obtain the following version of Lidskii theorem. Let L, M, N be p-dimensional subspaces in R^n. Let ψ_j be the angles between L and M, let ϕ_j be the angles between M and N, and let θ_j be the angles between L and N. Consider the orbit of the vector ψwith respect to permutations of coordinates and inversions of axises. Let Z be the convex hull of this orbit. Then θis an element of the polyhedron ϕ+ Z. We discuss similar theorems for other symmetric spaces. We obtain formula for geodesic distance for any invariant Finsler metrics on a classical Riemannian symmetric space.

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Yurii A. Neretin. 2000-05-06. On Jordan angles and triangle inequality in Grassmannian. https://doi.org/10.1023/a%3A1011974705094

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