论文标题
奇异子空间的条件数量，重新审视
The condition number of singular subspaces, revisited
论文作者
论文摘要
我从[J.-G.太阳，奇异子空间和放气子空间的扰动分析，numer。数学。 73（2），第235--263页，1996年]。对于真实且复杂的矩阵，我在矩阵的输入空间和弦，格拉斯曼和crocrusters在线性子空间的输出grassmannian歧管上的距离上介绍了此条件数的替代计算。该条件数量最多是一个小因素，等于对应于所选单数子空间的奇异值与未选择的奇异值之间的反比最小值差距。
I revisit the condition number of computing left and right singular subspaces from [J.-G. Sun, Perturbation analysis of singular subspaces and deflating subspaces, Numer. Math. 73(2), pp. 235--263, 1996]. For real and complex matrices, I present an alternative computation of this condition number in the Euclidean distance on the input space of matrices and the chordal, Grassmann, and Procrustes distances on the output Grassmannian manifold of linear subspaces. Up to a small factor, this condition number equals the inverse minimum singular value gap between the singular values corresponding to the selected singular subspace and those not selected.
