Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9498155 | Linear Algebra and its Applications | 2005 | 6 Pages |
Abstract
It is shown that, quite surprisingly, all matrices of the form LâMâ, where Lâ and Mâ denote generalized inverses of L and M, are generalized inverses of ML if and only if the product MLLâMâML is invariant with respect to the choice of Lâ and Mâ, which at the first glance looks to be a weaker condition than the requirement that MLLâMâMLÂ =Â ML for every Lâ and Mâ. This statement follows as an immediate corollary to the main result of the present note, which provides two criteria for the invariance of expressions of the type KLâMâN involving four given matrices K, L, M, N, with generalized inverses Lâ, Mâ of two of them.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Jerzy K. Baksalary, Oskar Maria Baksalary,