Note on the Generalized Inverse of the Product of Matrices

Previous article Next article Note on the Generalized Inverse of the Product of MatricesRandall E. ClineRandall E. Clinehttps://doi.org/10.1137/1006007PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout"Note on the Generalized Inverse of the Product of Matrices." SIAM Review, 6(1), pp. 57–58[1] R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc., 51 (1955), 406–413 MR0069793 0065.24603 CrossrefGoogle Scholar[2] T. N. E. Greville, The pseudoinverse of a rectangular or singular matrix and its application to the solution of systems of linear equations, SIAM Rev., 1 (1959), 38–43 10.1137/1001003 MR0101615 0123.11202 LinkISIGoogle Scholar[3] T. N. E. Greville, Some applications of the pseudoinverse of a matrix, SIAM Rev., 2 (1960), 15–22 10.1137/1002004 MR0110185 0168.13303 LinkISIGoogle Scholar[4] R. E. Cline, On the Computation of the Generalized Inverse, A+, of an Arbitrary Matrix, A, and the Use of Certain Associated Eigenvectors in Solving the Allocation Problem, Preliminary Report, Statistical and Computing Laboratory, Purdue University, 1958 Google Scholar[5] R. E. Cline, Masters Thesis, Representations for the Generalized Inverse of Matrices with Applications in Linear Programming, Doctoral Thesis, Purdue University, 1963 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Some additive results on M-P inverse of operator product18 October 2019 | Asian-European Journal of Mathematics, Vol. 14, No. 01 Cross Ref Identities concerning the reverse order law for the Moore–Penrose inverseApplied Mathematics and Computation, Vol. 220 Cross Ref Some results on the reverse order law in rings with involution14 March 2012 | Aequationes mathematicae, Vol. 83, No. 3 Cross Ref Note on the weighted generalized inverse of the product of matrices29 December 2009 | Journal of Applied Mathematics and Computing, Vol. 35, No. 1-2 Cross Ref MV-PURE Estimator: Minimum-Variance Pseudo-Unbiased Reduced-Rank Estimator for Linearly Constrained Ill-Conditioned Inverse ProblemsIEEE Transactions on Signal Processing, Vol. 56, No. 8 Cross Ref The construction of free–free flexibility matrices for multilevel structural analysisComputer Methods in Applied Mechanics and Engineering, Vol. 191, No. 19-20 Cross Ref Moore-Penrose Inverse of a Matrix Product with Normal Matrix11 February 2009 | Econometric Theory, Vol. 11, No. 3 Cross Ref Random Coefficient Models for Multilevel Analysis20 December 2016 | Journal of Educational Statistics, Vol. 11, No. 1 Cross Ref Computational methods of linear algebraJournal of Soviet Mathematics, Vol. 15, No. 5 Cross Ref On pseudoinverses of operator productsLinear Algebra and its Applications, Vol. 33 Cross Ref Annotated Bibliography on Generalized Inverses and Applications Cross Ref Mach Reflection Using Ray-Shock TheoryAIAA Journal, Vol. 13, No. 11 Cross Ref Practical Aspect of the Generalized Inverse of a MatrixAIAA Journal, Vol. 13, No. 11 Cross Ref References Cross Ref Das verallgemeinerte Inverse eines linearen Operators in Vektorräumen mit nicht ausgearteter Hermitescher Metrik über einenm kommutativen Körper.Journal für die reine und angewandte Mathematik (Crelles Journal), Vol. 1972, No. 252 Cross Ref An Extension of the Generalized Inverse of a Matrix12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 19, No. 4AbstractPDF (510 KB)Subclasses of generalized inverses of matricesAnnals of the Institute of Statistical Mathematics, Vol. 22, No. 1 Cross Ref Theorems on products of EPr matricesLinear Algebra and its Applications, Vol. 2, No. 1 Cross Ref A note on generalized inverses29 October 2013 | Naval Research Logistics Quarterly, Vol. 15, No. 4 Cross Ref On the Geometry of Subspaces in Euclidean n-Spaces13 July 2006 | SIAM Journal on Applied Mathematics, Vol. 15, No. 5AbstractPDF (964 KB)On the Fixed Point Probability Vector of Regular or Ergodic Transition MatricesJournal of the American Statistical Association, Vol. 62, No. 318 Cross Ref A Generalization of the Gauss-Markov TheoremJournal of the American Statistical Association, Vol. 61, No. 316 Cross Ref On the ``Reverse Order Law'' Related to the Generalized Inverse of Matrix ProductsJournal of the ACM, Vol. 13, No. 3 Cross Ref On Partial Isometries in Finite-Dimensional Euclidean Spaces28 July 2006 | SIAM Journal on Applied Mathematics, Vol. 14, No. 3AbstractPDF (994 KB)Il metodo di inversione generalizzata nella soluzione di problemi lineariCalcolo, Vol. 2, No. S1 Cross Ref An Alternate Form of the Generalized Inverse of an Arbitrary Complex Matri18 July 2006 | SIAM Review, Vol. 7, No. 3AbstractPDF (197 KB)Representations for the Generalized Inverse of Sums of Matrices3 August 2006 | Journal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis, Vol. 2, No. 1AbstractPDF (1047 KB) Volume 6, Issue 1| 1964SIAM Review History Submitted:31 October 1963Published online:18 July 2006 InformationCopyright © 1964 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1006007Article page range:pp. 57-58ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics