关键词: 
• 延拓矩阵,奇异值分解,奇异向量,Rayleigh商,奇异子空间.

摘要: 摘要：在知道母矩阵 和延拓矩阵 的奇异值分解下，导出了延拓矩阵 的Rayleigh商与母矩阵 的奇异值间的定量关系，得到了延拓矩阵 的Rayleigh商的近似奇异子空间的扰动界与母矩阵 的奇异值间的定量关系.Abstract: Knowing the singular value decompositions of the mother matrix and of extended matrix , the quantitative relationship between the Rayleigh quotient of the extended matrix and the singular value of the mother matrix is deduced, and the quantitative relationship between the perturbation bound of the approximation singular subspace of the Rayleigh quotient of the extended matrix and the singular value of the mother matrix is got .