On Jordan angles and triangle inequality in Grassmannian
arXiv:math/0005059 · doi:10.1023/A:1011974705094
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.
12 pages