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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