Takane, Yoshio; Yanai, Haruo On oblique projectors. (English) Zbl 0930.15003 Linear Algebra Appl. 289, No. 1-3, 297-310 (1999). Two problems regarding oblique projectors are discussed. One is concerned with products of two oblique projectors and the other with decompositions of oblique projectors. The first problem relates to the determination of the onto- and the along-spaces of a product of two oblique projectors under various conditions. The second problem involves the decomposition of oblique projectors, when both predictor variables and instrumental variables consist of two distinct sets of variables. Reviewer: Váslaw Burjan (Praha) Cited in 1 ReviewCited in 16 Documents MSC: 15A03 Vector spaces, linear dependence, rank, lineability 15A09 Theory of matrix inversion and generalized inverses Keywords:vector spaces; matrix inversion; oblique projectors; decompositions PDF BibTeX XML Cite \textit{Y. Takane} and \textit{H. Yanai}, Linear Algebra Appl. 289, No. 1--3, 297--310 (1999; Zbl 0930.15003) Full Text: DOI OpenURL References: [1] Brown, A.L.; Page, A., Elements of functional analysis, (1970), Van Nostrand New York · Zbl 0199.17902 [2] Groß, J.; Trenkler, G., On the product of oblique projectors, Linear and multilinear algebra, 30, 1-13, (1998) [3] Johnston, J., Econometric methods, (1984), McGraw-Hill New York [4] Khatri, C.G., Some results for singular multivariate regression models, Sankhya¯, 30, 267-280, (1968) · Zbl 0177.22802 [5] Rao, C.R.; Mitra, S.K., Generalized inverse of matrices and its application, (1971), Wiley New York [6] Rao, C.R.; Yanai, H., General definition and decomposition of projectors and some applications to statistical problems, Journal of statistical planning and inference, 3, 1-17, (1979) · Zbl 0427.62046 [7] Takane, Y.; Yanai, H.; Mayekawa, S., Relationships among various methods of linearly constrained correspondence analysis, Psychometrika, 56, 667-684, (1991) · Zbl 0760.62057 [8] Werner, H.J., G-inverses of matrix products, (), 531-546 · Zbl 0794.15001 [9] Yanai, H., Some generalized forms of least squares g-inverse, minimum norm g-inverse and Moore-Penrose g-inverse matrices, Computational statistics and data analysis, 10, 251-260, (1990) · Zbl 0825.62550 [10] Yanai, H.; Takane, Y., Canonical correlation analysis with linear constraints, Linear algebra and its applications, 176, 75-89, (1992) · Zbl 0766.62033 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.