Inverses of Rank Invariant Powers of a Matrix
Randall E. Cline · SIAM Journal on Numerical Analysis · 1968
Previous article Inverses of Rank Invariant Powers of a MatrixRandall E. ClineRandall E. Clinehttps://doi.org/10.1137/0705015PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Randall E. Cline, Representations for the generalized inverse of a partitioned matrix, J. Soc. Indust. Appl. Math., 12 (1964), 588–600 10.1137/0112050 MR0172890 0166.29902 LinkISIGoogle Scholar[2] Randall E. Cline, Representations for the generalized inverse of sums of matrices, J. Soc. Indust. Appl. Math. Ser. B. Numer. Anal., 2 (1965), 99–114 MR0180572 0142.26904 LinkGoogle Scholar[3] R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc., 51 (1955), 406–413 MR0069793 0065.24603 CrossrefGoogle Scholar[4] Charles A. Rohde, Generalized inverses of partitioned matrices, J. Soc. Indust. Appl. Math., 13 (1965), 1033–1035 10.1137/0113070 MR0190161 0145.03801 LinkISIGoogle Scholar[5] A. J. Goldman and , M. Zelen, Weak generalized inverses and minimum variance linear unbiased estimation, J. Res. Nat. Bur. Standards Sect. B, 68B (1964), 151–172 MR0173312 0127.35703 CrossrefISIGoogle Scholar[6] M. P. Drazin, Pseudo-inverses in associative rings and semigroups, Amer. Math. Monthly, 65 (1958), 506–514 MR0098762 0083.02901 CrossrefGoogle Scholar[7] R. E. Cline, An application of representations for the generalized inverse of a matrix, Tech. Summary Rep., 592, Mathematics Research Center, U. S. Army, University of Wisconsin, Madison, 1965 Google Scholar[8] 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 Previous article FiguresRelatedReferencesCited ByDetails Displacement structure of the core inverseLinear and Multilinear Algebra, Vol. 70, No. 2 | 23 January 2020 Cross Ref Representations of the weighted WG inverse and a rank equation's solutionLinear and Multilinear Algebra, Vol. 58 | 11 January 2022 Cross Ref New classes of more general weighted outer inversesLinear and Multilinear Algebra, Vol. 70, No. 1 | 16 January 2020 Cross Ref Further results on the Drazin inverse of even‐order tensorsNumerical Linear Algebra with Applications, Vol. 27, No. 5 | 7 August 2020 Cross Ref Core and core-EP inverses of tensorsComputational and Applied Mathematics, Vol. 39, No. 1 | 29 October 2019 Cross Ref Integration enhanced and noise tolerant ZNN for computing various expressions involving outer inversesNeurocomputing, Vol. 329 | 1 Feb 2019 Cross Ref USSOR methods for solving the rank deficient linear least squares problemCalcolo, Vol. 54, No. 1 | 7 March 2016 Cross Ref Computing {2,4} and {2,3}-inverses by using the Sherman–Morrison formulaApplied Mathematics and Computation, Vol. 273 | 1 Jan 2016 Cross Ref Core inverse and core partial order of Hilbert space operatorsApplied Mathematics and Computation, Vol. 244 | 1 Oct 2014 Cross Ref New representations of the Moore–Penrose inverse of 2×2 block matricesLinear Algebra and its Applications, Vol. 456 | 1 Sep 2014 Cross Ref A short proof of a matrix decomposition with applicationsLinear Algebra and its Applications, Vol. 438, No. 3 | 1 Feb 2013 Cross Ref Gauss–Jordan elimination method for computing outer inversesApplied Mathematics and Computation, Vol. 219, No. 9 | 1 Jan 2013 Cross Ref A modified Cp statistic in a system-of-equations modelJournal of Statistical Planning and Inference, Vol. 142, No. 8 | 1 Aug 2012 Cross Ref Full-rank representations of outer inverses based on the QR decompositionApplied Mathematics and Computation, Vol. 218, No. 20 | 1 Jun 2012 Cross Ref AOR iterative methods for rank deficient least squares problemsJournal of Applied Mathematics and Computing, Vol. 26, No. 1-2 | 5 January 2008 Cross Ref On accelerate overrelaxation methods for rank deficient linear systemsApplied Mathematics and Computation, Vol. 173, No. 2 | 1 Feb 2006 Cross Ref Symmetric successive overrelaxation methods for rank deficient linear systemsApplied Mathematics and Computation, Vol. 173, No. 1 | 1 Feb 2006 Cross Ref Symmetric successive overrelaxation methods for solving the rank deficient linear least squares problemApplied Mathematics and Computation, Vol. 169, No. 2 | 1 Oct 2005 Cross Ref On the Moore–Penrose generalized inverse matrixApplied Mathematics and Computation, Vol. 158, No. 1 | 1 Oct 2004 Cross Ref Accelerate overrelaxation methods for rank deficient linear systemsApplied Mathematics and Computation, Vol. 140, No. 2-3 | 1 Aug 2003 Cross Ref Full-rank and determinantal representation of the Drazin inverseLinear Algebra and its Applications, Vol. 311, No. 1-3 | 1 May 2000 Cross Ref Limit representations of generalized inverses and related methodsApplied Mathematics and Computation, Vol. 103, No. 1 | 1 Aug 1999 Cross Ref Categorical methods in linear algebraLinear Algebra and its Applications, Vol. 167 | 1 Apr 1992 Cross Ref Bordered Matrices, Singular Systems, and Ergodic Markov ChainsKing-Wah Eric ChuSIAM Journal on Scientific and Statistical Computing, Vol. 11, No. 4 | 13 July 2006AbstractPDF (1523 KB)Successive overrelaxation methods for solving the rank deficient linear squares problemLinear Algebra and its Applications, Vol. 88-89 | 1 Apr 1987 Cross Ref Generalized inverses of matrices: a perspective of the work of PenroseMathematical Proceedings of the Cambridge Philosophical Society, Vol. 100, No. 3 | 24 October 2008 Cross Ref More on generalizations of matrix monotonicityLinear Algebra and its Applications, Vol. 48 | 1 Dec 1982 Cross Ref Nonnegative integral generalized inversesLinear Algebra and its Applications, Vol. 39 | 1 Aug 1981 Cross Ref Nonnegative $\lambda $-Monotone MatricesS. 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