M-P逆在非保秩扰动下半正定极因子的扰动界

Perturbation Bounds of Semi-definite Positive Factors of M-P Inverse under Non-Preserving Rank Perturbating

设A+和+的广义极分解分别是A+=QH与+=■■,其中H与■为n×m半正定因子,利用奇异值分解的方法、酉不变范数‖·‖和Frobenius范数‖·‖F,研究了Moore-Penrose广义逆矩阵A+在非保秩扰动下半正定极因子的扰动界.

Suppose the generalized polar decomposition of A ^＋ and A^-＋ are respectively A^＋ = QH and A^-＋ = QH^- and H and H are n × m semi-definite positive factors. By using singular-value decomposition, unitarily invariant norm ｜｜ ·｜｜ and Frobenius norm ｜｜ ·｜｜ r, the perturbation bound of semi-definite polar factors of Moore-Penrose generalized inverse matrix A ^＋ under non-preserving rank perturbating is researched.