酉不变范数下广义极分解的扰动界

Perturbation Bounds of Generalized Polar Decomposition under Unitarily Invariant Norms

设A是m×n且秩为r的复矩阵,存在m×n次酉矩阵Q和n×n半正定矩阵H使得A=QH.此分解称为A的广义极分解.文章给出了在任意酉不变范数下次酉矩阵Q和半正定矩阵H的扰动界.

Let A be an m ×n complex matrix, whose rank is r. It is well-known that there is a generalized polar decomposition A=QH, where Q is an n×n subunitary matrix, and H is a Hermite positive semidefinite matrix. Perturbati on bounds are obtained of the Hermite positive semidefinite matrix under the general unitarily invariant norm.