M-P逆在加法扰动下半正定极因子的扰动界

Perturbation Bounds for Semi-positive Definite Polar Factor of M-P Inverse under Additive Noise

设A∈Cmr×n,~A∈Cmr×n,则A+∈Crn×m,~A+∈Cnr×m.A+和~A+的广义极分解分别是A+=QH与~A+=~Q^H,其中H与~H为n×m次酉矩阵,利用奇异值分解的方法,给出了Moore-Penrose广义逆矩阵A+在酉不变范数‖.‖下半正定极因子的扰动界.

Let A∈Cτ^m×n and ^~A∈Cτ^m×n,then A^＋∈Cτ^n×m and ^~A∈Cτ^n×m. The generalized polar decompositions of A^＋ and A^＋=QH and ^~A^＋=^~Q^~H respectively.The H and ^~H are n×m sub - unitary matrix. With the singular value decomposition, the perturbation bounds for semi - positive defmite polar factor of Moore - Penrose generalized inverse matrix A^＋ under unitarily invariant norm ‖·‖ are obtained.