Mixed-type reverse order law of
β Scribed by Minghui Wang; Musheng Wei; Zhigang Jia
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 133 KB
- Volume
- 430
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
β¦ Synopsis
Some mixed-type reverse-order laws of (AB) β have been proposed and studied by Tian. In this paper, by applying the extremal rank relations of generalized Schur complements and the P-SVD of two matrices A and B, we study two kind of mixed-type reverse-order laws for (AB) (13) , obtain necessary and sufficient conditions for these reverse-order laws.
π SIMILAR VOLUMES
In this paper, we offer purely algebraic necessary and sufficient conditions for reverse order laws for generalized inverses in C\*algebras, extending rank conditions for matrices and range conditions for Hilbert space operators.
It is shown that, quite surprisingly, all matrices of the form L -M -, where L -and M - denote generalized inverses of L and M, are generalized inverses of ML if and only if the product MLL -M -ML is invariant with respect to the choice of L -and M -, which at the first glance looks to be a weaker c