矩阵在等价分解下的Penrose型广义逆的通式(英文)

THE GENERAL FORMS FOR PENROSE-INVERSES OF A MATRIX UNDER THE EQUIVALENCE DECOMPOSTION

设A∈Rrm×n,本文讨论了矩阵A在等价分解下的13类Moore-Penrose型广义逆的通式.由于等价分解是矩阵论及其应用中的一种重要的分解,并且本文所给出的通式只需通过矩阵的初等变换和乘法运算就能得到,故这些通式在相关的理论研究和实际应用中是有一定价值的.

We provide the general forms of Penrose-inverses of a real matrix under the matrix equivalence decomposition.The general forms are useful since the matrix equivalence decomposition is important in matrix theory and its applications,and the new general forms under the decomposition can be obtained easily in many cases.