A Note on Pseudoinverses
C. Desoer, B. H. Whalen · Journal of the Society for Industrial and Applied Mathematics · 1963
Previous article Next article A Note on PseudoinversesC. A. Desoer and B. H. WhalenC. A. Desoer and B. H. Whalenhttps://doi.org/10.1137/0111031PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] E. H. Moore, General Analysis, Part 1, Memoirs, Amer. Philos. Soc., 1 (1935), 147–209 0013.11605 Google Scholar[2] E. H. Moore, , Bulletin Amer. Math. Soc., 26 (1920), 394–395 Google Scholar[3] R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc., 51 (1955), 406–413 MR0069793 0065.24603 CrossrefGoogle Scholar[4] R. Penrose, On best approximation solutions of linear matrix equations, Proc. Cambridge Philos. Soc., 52 (1956), 17–19 MR0074092 0070.12501 CrossrefGoogle Scholar[5] 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[6] 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[7] R. E. Kalman, , Y. C. Ho and , K. S. Narenda, Controllability of linear dynamical systems, Contributions to Differential Equations, Vol. I, Interscience Publishers, Inc., New York, 1962 Google Scholar[8] R. E. Kalman, New methods and results in linear prediction and filtering theory, Tech. Report, 61-1, RIAS Google Scholar[9] Nelson Dunford and , Jacob T. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York, 1958xiv+858 MR0117523 0084.10402 Google Scholar[10] Frigyes Riesz and , Béla Sz.-Nagy, Functional analysis, Frederick Ungar Publishing Co., New York, 1955xii+468 MR0071727 Google Scholar[11] Angus E. Taylor, Introduction to functional analysis, John Wiley & Sons Inc., New York, 1958xvi+423 MR0098966 0081.10202 Google Scholar[12] Bernard Friedman, Principles and techniques of applied mathematics, John Wiley & Sons Inc., New York, 1956ix+315 MR0079181 0072.12806 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Generalized Inverses of a Bordered Matrix of OperatorsSIAM Journal on Applied Mathematics, Vol. 29, No. 1 | 12 July 2006AbstractPDF (838 KB)The Pseudo-Inverse of a ProductSIAM Journal on Applied Mathematics, Vol. 24, No. 4 | 17 February 2012AbstractPDF (669 KB)On the Convergence of the Conjugate Gradient Method for Singular Linear Operator EquationsSIAM Journal on Numerical Analysis, Vol. 9, No. 1 | 1 August 2006AbstractPDF (1764 KB)On the Classification of Matrix Generalized InversesSIAM Review, Vol. 12, No. 4 | 18 July 2006AbstractPDF (356 KB)Steepest Descent for Singular Linear Operator EquationsSIAM Journal on Numerical Analysis, Vol. 7, No. 3 | 14 July 2006AbstractPDF (432 KB)A Restricted Pseudoinverse and Its Application to Constrained MinimaSIAM Journal on Applied Mathematics, Vol. 19, No. 1 | 12 July 2006AbstractPDF (910 KB)On Some Representations of Generalized InversesSIAM Review, Vol. 11, No. 2 | 18 July 2006AbstractPDF (278 KB)An Oblique Matrix PseudoinverseSIAM Journal on Applied Mathematics, Vol. 16, No. 5 | 28 July 2006AbstractPDF (1207 KB)An Alternate Definition of a Pseudoinverse of a MatrixSIAM Journal on Applied Mathematics, Vol. 14, No. 4 | 3 August 2006AbstractPDF (1383 KB)On Partial Isometries in Finite-Dimensional Euclidean SpacesSIAM Journal on Applied Mathematics, Vol. 14, No. 3 | 28 July 2006AbstractPDF (994 KB)A Method for Computing Least Squares Estimators that Keep Up with the DataJournal of the Society for Industrial and Applied Mathematics Series A Control, Vol. 3, No. 3 | 18 July 2006AbstractPDF (2356 KB) Volume 11, Issue 2| 1963Journal of the Society for Industrial and Applied Mathematics205-519 History Submitted:20 April 1962Accepted:30 November 1962Published online:13 July 2006 InformationCopyright © 1963 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0111031Article page range:pp. 442-447ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics