Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6416660 | Linear Algebra and its Applications | 2013 | 21 Pages |
Abstract
For two positive definite adjointable operators M and N, and an adjointable operator A acting on a Hilbert Câ-module, some properties of the weighted Moore-Penrose inverse AMNâ are established. If A=(Aij) is 1Â ÃÂ 2 or 2Â ÃÂ 2 partitioned, then general representations for AMNâ in terms of the individual blocks of Aij are studied. In the case when A is 1Â ÃÂ 2 partitioned, a unified representation for AMNâ is presented. In the 2Â ÃÂ 2 partitioned case, an approach to the construction of the Moore-Penrose inverse from the non-weighted case to the weighted case is provided. Some results known for matrices are extended to the general setting of operators on Hilbert Câ-modules.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Qingxiang Xu, Yonghao Chen, Chuanning Song,