On the angular metrics between linear subspaces (Q864565)

It has been recently shown by the authors that the symmetric gauge functions on the canonical (principal) angles give a family of unitarily invariant metrics between linear subspaces of the same dimension. In this paper, such metrics are extended to subspaces of possibly different dimensions. Also, the authors conjecture that the angular metrics give all unitarily invariant intrinsic metrics on the Grassmanian manifold \({\mathcal G}_{m,n}\) of \(m\)-dimensional subspaces of~\({\mathbb C}^n\).