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Title: Unitarily invariant metrics on the Grassmann space
Authors: Qiu, Li
Zhang, Yanxia
Li, Chi-Kwong
Keywords: Unitarily invariant metric
Grassmann space
Symmetric gauge function
Canonical angles
Triangular inequality
Issue Date: 2004
Abstract: It is shown that Φ(θ1(Χ, Y),...,θm(Χ, Y)) defines a unitarily invariant metric on the Grassmann space Gm,n of m-dimensional subspaces of Fn for every symmetric gauge function Φ, where θ1(Χ, Y),...,θm(Χ, Y) are the canonical angles between subspaces X, Y ∈ Gm,n. This provides a wide class of new metrics on Gm,n. Some related results on perturbation and approximation of subspaces in Gm,n, as well as the canonical angles between them, are also discussed. Furthermore, the equality case of the triangular inequality for several unitarily invariant metrics are analyzed.
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