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.

翻译：在Grassmannian 输出空间的输入空间和 chordal、 Frobenius 和 procrustes 距离的Frobenius 规范中确定了计算与矩阵单值的任何选定子集相对应的左方或右单位子空间的条件编号。在小系数中,该条件编号等于投影器选定的单值与未选中的单值之间的反最小单值差,包括任何幽灵单值。