The condition number of singular subspaces

The condition number of computing the invariant left or right singular subspace corresponding to any selected subset of singular values of matrices is determined in the Frobenius norm on the input space of matrices and the chordal, Frobenius, and Procrustes distances on the Grassmannian output space. Up to a small factor, this condition number equals the inverse minimum singular value gap between the singular values selected by the projector and those not selected, including any ghost singular values.