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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Takane, Y., Tian, Y. & Yanai, H. On constrained generalized inverses of matrices and their properties. AISM 59, 807–820 (2007). https://doi.org/10.1007/s10463-006-0075-3
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DOI: https://doi.org/10.1007/s10463-006-0075-3