On constrained generalized inverses of matrices and their properties |
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| Authors: | Yoshio Takane Yongge Tian Haruo Yanai |
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| Institution: | (1) Department of Psychology, McGill University, Montréal, QC, H3A 1B1, Canada;(2) School of Economics, Shanghai University of Finance and Economics, Shanghai, 200433, China;(3) St. Luke’s College of Nursing, Chuo-ku, Tokyo, Japan |
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| Abstract: | A matrix G is called a generalized inverse (g-invserse) of matrix A if AGA = A and is denoted by G = A
−. Constrained g-inverses of A are defined through some matrix expressions like E(AE)−, (FA)−
F and E(FAE)−
F. In this paper, we derive a variety of properties of these constrained g-inverses by making use of the matrix rank method. As applications, we give some results on g-inverses of block matrices, and weighted least-squares estimators for the general linear model. |
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| Keywords: | Linear matrix expression Moore– Penrose inverse Constrained generalized inverses Matrix equation Projector Idempotent matrix Rank equalities General linear model Weighted least-squares estimator |
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