矩阵的半正定因子及次酉极因子的扰动界

Perturbation Bounds for the Semi-definite Factors and Subunitary Polar Factors

在矩阵的扰动分析中,广义极分解和奇异值分解占有非常重要的地位。对矩阵进行广义极分解,得到半正定因子和次酉极因子。利用矩阵的奇异值分解和广义极分解,得到了范数意义下矩阵的半正定因子和次酉极因子的扰动界,且扰动界是以恒等式的形式给出。

The generalized polar decomposition and singular value decomposition play a very important role in the analysis of the perturbation of the matrix. The positive semi definite factor and the sub unitary polar factor are obtained through the generalized polar decomposition of the matrix. By using the singular value decomposition and the generalized polar decomposition of matrix, obtained the perturbation bounds for the semi-definite factor and the subunitary polar factor in the sense of F-norm, and the perturbation bounds are given in the form of the identities.