矩阵广义逆的一个混合反序律

A Mixed-Type Reverse Order Law for Generalized Inverse of a Triple Matrix Product

使用矩阵三元组(A,B,C)的乘积型广义奇异值分解,证明了总是存在广义逆矩阵A^((1,2,3)),B^((1,2))和C^((1,2,4)),使得矩阵乘积ABC的Moore-Penrose逆可以表示成如下形式(ABC)^+=C^((1,2,4))B^((1,2))A^((1,2,3)).所获结果是Wibker,Howe和Gilbert的结果的自然推广.

For the triple matrix product ABC, we show through the product-product singular value decomposition of matrix triplets （A, B, C） that there exist three general- ized inverses A^（1,2,3）, B^（1,2） and C^（1,2,4） such that the Moore-Penrose inverse of ABC can be expressed as （ABC）^t = C^（1,2,4）B^（1,2）A^（1,2,3）. The results are the generalization of results obtained by Wibker, Howe and Gilbert.