SFB 303 Discussion Paper No. B - 257

Author: Werner, Hans Joachim
Title: G-Inverses of Matrix Products
Abstract: Let A and B be complex matrices such that AB exists. As is well known, the reverse order law does not always hold for Moore-Penrose inversion, that is, (AB)- is not always B-A-. In this paper several results of a reverse order law type relative to the more general setting of generalized inversion are established. In practice factorizations of a g-inverse often arise from factorizations of the matrix which is to be inverted. In addition to full rank factorizations, normal factorizations and singular value decompositions (SVD) there are other factorizations of particular matrices that are natural to certain problems, e.g. in statistics. Answers to the problems discussed in this paper may thus be a computational tool. Besides they are of significant interest in the basic theory of g-inversion because they provide us with intrinsic insights into the g-inversion of matrix products.
Keywords: Moor-Penrose inversion, Reverse order law, G-inversion
JEL-Classification-Number: C1, C3
Creation-Date: 1992
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