An Alternate Definition of a Pseudoinverse of a Matrix
James E. Scroggs, Patrick L. Odell · SIAM Journal on Applied Mathematics · 1966
Previous article Next article An Alternate Definition of a Pseudoinverse of a MatrixJames E. Scroggs and Patrick L. OdellJames E. Scroggs and Patrick L. Odellhttps://doi.org/10.1137/0114067PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. Ben-Israel and , A. Charnes, Contributions to the theory of generalized inverses, J. Soc. Indust. Appl. Math., 11 (1963), 667–699 10.1137/0111051 MR0179192 (31:3441) 0116.32202 LinkISIGoogle Scholar[2] C. A. Desoer and , B. H. Whalen, A note on pseudoinverses, J. Soc. Indust. Appl. Math., 11 (1963), 442–447 10.1137/0111031 MR0156199 (27:6128) 0123.09603 LinkISIGoogle Scholar[3] M. P. Drazin, Pseudo-inverses in associative rings and semigroups, Amer. Math. Monthly, 65 (1958), 506–514 MR0098762 (20:5217) 0083.02901 CrossrefGoogle Scholar[4] D. K. Faddeev and , V. N. Faddeeva, Computational methods of linear algebra, Translated by Robert C. Williams, W. H. Freeman and Co., San Francisco, 1963xi+621 MR0158519 (28:1742) Google Scholar[5] K. O. Friedrichs, Functional Analysis, Mimeographed lecture notes, New York University, New York, 1950 Google Scholar[6] F. R. Gantmacher, Applications of the theory of matrices, Translated by J. L. Brenner, with the assistance of D. W. Bushaw and S. Evanusa, Interscience Publishers, Inc., New York, 1959ix+317 MR0107648 (21:6372b) 0085.01001 Google Scholar[7] C. Lanczos, Linear systems in self-adjoint form, Amer. Math. Monthly, 65 (1958), 665–679 MR0103196 (21:1978) 0083.00604 CrossrefGoogle Scholar[8] E. H. Moore, General Analysis, Part I, Mem. Amer. Philos. Soc., 1 (1935), 0013.11605 Google Scholar[9] R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc., 51 (1955), 406–413 MR0069793 (16,1082a) 0065.24603 CrossrefGoogle Scholar[10] R. D. Sheffield, On pseudo inverses of linear transformations in Banach spaces, Report, 2133, Oak Ridge National Laboratory, 1956 Google Scholar[11] R. D. Sheffield, A general theory for linear systems, Amer. Math. Monthly, 65 (1958), 109–111 MR0096694 (20:3177) 0082.02101 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Stationary and Time-Dependent Molecular Distributions in Slow-Fast Feedback CircuitsPavol BokesSIAM Journal on Applied Dynamical Systems, Vol. 21, No. 2 | 13 April 2022AbstractPDF (1543 KB)Efficient algorithm for finding the inverse and the group inverse of FLSr-circulant matrixJournal of Applied Mathematics and Computing, Vol. 18, No. 1-2 | 1 Mar 2005 Cross Ref Noncore square matrices miscellanyLinear Algebra and its Applications, Vol. 249, No. 1-3 | 1 Dec 1996 Cross Ref Matrix partial orders through generalized inverses: unified theoryLinear Algebra and its Applications, Vol. 148 | 1 Apr 1991 Cross Ref Computational methods of linear algebraJournal of Soviet Mathematics, Vol. 15, No. 5 | 1 Jan 1981 Cross Ref Weak Drazin inversesLinear Algebra and its Applications, Vol. 20, No. 2 | 1 Jan 1978 Cross Ref Solution of Degnerate Linear Initial Value ProblemsZAMM - Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 57, No. 2 | 1 Jan 1977 Cross Ref Annotated Bibliography on Generalized Inverses and ApplicationsGeneralized Inverses and Applications | 1 Jan 1976 Cross Ref Concerning Spectral Inverses of Stochastic MatricesD. J. HartfielSIAM Journal on Applied Mathematics, Vol. 27, No. 2 | 12 July 2006AbstractPDF (797 KB)Generalized inverses of certain Toeplitz matricesLinear Algebra and its Applications, Vol. 8, No. 1 | 1 Feb 1974 Cross Ref Theory and Application of Constrained Inverse of MatricesC. Radhakrishna Rao and Sujit Kumar MitraSIAM Journal on Applied Mathematics, Vol. 24, No. 4 | 17 February 2012AbstractPDF (1466 KB)Spectral Inverses of Stochastic MatricesJ. R. Wall and R. J. PlemmonsSIAM Journal on Applied Mathematics, Vol. 22, No. 1 | 12 July 2006AbstractPDF (440 KB)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 | 1 Jan 1972 Cross Ref Generalized Inverses, Normal Solvability, and Iteration for Singular Operator EquationsNonlinear Functional Analysis and Applications | 1 Jan 1971 Cross Ref A Restricted Pseudoinverse and Its Application to Constrained MinimaNariyasu Minamide and Kahei NakamuraSIAM Journal on Applied Mathematics, Vol. 19, No. 1 | 12 July 2006AbstractPDF (910 KB)On Matrices of Index Zero or OneAdi Ben-IsraelSIAM Journal on Applied Mathematics, Vol. 17, No. 6 | 17 February 2012AbstractPDF (254 KB)A Note on the Scroggs—Odell PseudoinverseT. L. Boullion and P. L. OdellSIAM Journal on Applied Mathematics, Vol. 17, No. 1 | 28 July 2006AbstractPDF (278 KB)An Oblique Matrix PseudoinverseR. D. MilneSIAM Journal on Applied Mathematics, Vol. 16, No. 5 | 28 July 2006AbstractPDF (1207 KB)Pseudoinverss of Postive Semidefeinite MatricesT. O. Lewis and T. G. NewmanSIAM Journal on Applied Mathematics, Vol. 16, No. 4 | 12 July 2006AbstractPDF (320 KB) Volume 14, Issue 4| 1966SIAM Journal on Applied Mathematics641-959 History Submitted:27 January 1964Accepted:15 November 1965Published online:03 August 2006 InformationCopyright © 1966 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0114067Article page range:pp. 796-810ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics