On Construction and Properties of the Generalized Inverse
Armen G. Fisher · SIAM Journal on Applied Mathematics · 1967
Previous article Next article On Construction and Properties of the Generalized InverseArmen G. FisherArmen G. Fisherhttps://doi.org/10.1137/0115026PDFBibTexSections 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 0116.32202 LinkISIGoogle Scholar[2] John S. Chipman, On least squares with insufficient observations, J. Amer. Statist. Assoc., 59 (1964), 1078–1111 MR0175220 0144.42401 CrossrefISIGoogle Scholar[3] 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[4] A. G. Fisher, Masters Thesis, Some techniques for analysis and interpretation of estimable functions in incomplete fixed factor designs, Doctoral thesis, Rutgers University, 1966 Google 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] 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] T. N. E. Greville, Note on fitting of functions of several independent variables, J. Soc. Indust. Appl. Math., 9 (1961), 109–115; erratum, 317 MR0129112 0168.14902 ISIGoogle Scholar[8] Peter W. M. John, Pseudo-inverses in the analysis of variance, Ann. Math. Statist., 35 (1964), 895–896 MR0162315 0123.36705 CrossrefISIGoogle Scholar[9] Marvin Marcus and , Henryk Minc, A survey of matrix theory and matrix inequalities, Allyn and Bacon Inc., Boston, Mass., 1964, 34– MR0162808 0126.02404 Google Scholar[10] R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc., 51 (1955), 406–413 MR0069793 0065.24603 CrossrefGoogle Scholar[11] Charles M. Price, The matrix pseudo-inverse and minimal variance estimates, SIAM Rev., 6 (1964), 115–120 10.1137/1006029 MR0169369 0125.37202 LinkISIGoogle Scholar[12] C. Radhakrishna Rao, Linear statistical inference and its applications, John Wiley & Sons Inc., New York, 196524–30, 183, 189 MR0221616 0137.36203 Google Scholar[13] C. Radhakrishna Rao, A note on a generalized inverse of a matrix with applications to problems in mathematical statistics, J. Roy. Statist. Soc. Ser. B, 24 (1962), 152–158 MR0138149 0121.14502 Google Scholar[14] 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 Previous article Next article FiguresRelatedReferencesCited ByDetails BibliographyHadamard Transform Optics | 1 Jan 1979 Cross Ref Some Topics in Generalized Inverses of MatricesGeneralized Inverses and Applications | 1 Jan 1976 Cross Ref Annotated Bibliography on Generalized Inverses and ApplicationsGeneralized Inverses and Applications | 1 Jan 1976 Cross Ref Existence and representation of diophantine and mixed diophantine solutions to linear equations and inequalitiesDiscrete Mathematics, Vol. 11, No. 3 | 1 Jan 1975 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 | 1 Jan 1972 Cross Ref On Ranks of PseudoinversesCarl D. Meyer, Jr.SIAM Review, Vol. 11, No. 3 | 2 August 2006AbstractPDF (207 KB)The Nature of the Lack of Uniqueness of Generalized Inverse MatricesN. S. UrquhartSIAM Review, Vol. 11, No. 2 | 18 July 2006AbstractPDF (316 KB)Computation of Generalized Inverse Matrices which Satisfy Specified ConditionsN. S. UrquhartSIAM Review, Vol. 10, No. 2 | 18 July 2006AbstractPDF (273 KB) Volume 15, Issue 2| 1967SIAM Journal on Applied Mathematics History Submitted:06 June 1966Published online:13 July 2006 InformationCopyright © 1967 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0115026Article page range:pp. 269-272ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics