Zheng, Bing ; Bapat, R. B. (2004) Characterization of generalized inverses by a rank equation Applied Mathematics and Computation, 151 (1). pp. 53-67. ISSN 0096-3003
Full text not available from this repository.
Official URL: http://linkinghub.elsevier.com/retrieve/pii/S00963...
Related URL: http://dx.doi.org/10.1016/S0096-3003(03)00322-9
Abstract
If A is a nonsingular matrix of order n and if B=C=In, then the inverse of A is the unique matrix X such that rank (ACBX ) = rank(A). In this paper, we generalize this fact to any matrix A of dimension m×n over the complex field to obtain analogous results for outer inverses of A. The converse problem is also considered in the sense that B and C are characterized when Ad,A#, A(1,2), A(1,2,3)and A(1,2,4)are solutions to this equation, respectively. This contributes to certain recent results in the literature, including that obtained by Groß [Linear Algebra Appl. 289 (1999) 127].
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Elsevier Science. |
| Keywords: | Rank Equation; Outer Inverse; Core-nilpotent Decomposition; Singular Value Decomposition |
| ID Code: | 1443 |
| Deposited On: | 04 Oct 2010 11:15 |
| Last Modified: | 13 May 2011 08:08 |
Repository Staff Only: item control page
