Journal
LINEAR ALGEBRA AND ITS APPLICATIONS
Volume 372, Issue -, Pages 207-224Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/S0024-3795(03)00508-1
Keywords
rank-one-modification; generalized inverse; idempotent matrix; orthogonal projector; oblique projector; semi-magic square
Categories
Ask authors/readers for more resources
Formulae for the Moore-Penrose inverse M+ of rank-one-modifications of a given m x n complex matrix A to the matrix M = A + bc*, where b and c* are nonzero m x 1 and 1 x n complex vectors, are revisited. An alternative to the list of such formulae, given by Meyer [SIAM J. Appl. Math. 24 (1973) 315] in forms of subtraction-addition type modifications of A(+), is established with the emphasis laid on achieving versions which have universal validity and are in a strict correspondence to characteristics of the relationships between the ranks of M and A. Moreover, possibilities of expressing M+ as multiplication type modifications of A(+), with multipliers required to be projectors, are explored. In the particular case, where A is nonsingular and the modification of A to M reduces the rank by 1, such a possibility was pointed out by Trenkler [R.D.H. Heijmans, D.S.G. Pollock, A. Satorra (Eds.), Innovations in Multivariate Statistical Analysis. A Festschrift for Heinz Neudecker, Kluwer, London, 2000, p. 67]. Some applications of the results obtained to various branches of mathematics are also discussed. (C) 2003 Elsevier Inc. All rights reserved.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available