Some Results on Generalized Inverses

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Previous article Next article Some Results on Generalized InversesCharles A. RohdeCharles A. Rohdehttps://doi.org/10.1137/1008040PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] R. C. Bose, Lecture Notes on Analysis of Variance, University of North Carolina, Chapel Hill, North Carolina, 1959 Google Scholar[2] J. S. Frame, Matrix functions and applications. I. Matrix operations and generalized inverses, IEEE Spectrum, 1 (1964), 209–220, (March) MR0183716 CrossrefGoogle Scholar[3] E. H. Moore, Abstract, Bull. Amer. Math. Soc., 26 (1920), 394–395 Google Scholar[4] R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc., 51 (1955), 406–413 MR0069793 0065.24603 CrossrefGoogle Scholar[5] 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[6] 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[7] C. A. Rohde, Masters Thesis, Contributions to the theory, computation and applications of generalized inverses, Ph.D. Dissertation, North Carolina State University, Raleigh, 1964 Google Scholar[8] M. Zelen and , A. J. Goldman, Weak generalized inverses and minimum variance linear unbiased estimation, Tech. Report, 314, Mathematics Research Center, United States Army, University of Wisconsin, Madison, 1963 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Literature Cited29 August 2012 Cross Ref A modified Cp statistic in a system-of-equations modelJournal of Statistical Planning and Inference, Vol. 142, No. 8 Cross Ref The First Problem of Algebraic Regression21 December 2011 Cross Ref The Fifth Problem of Probabilistic Regression21 December 2011 Cross Ref The Nonlinear Problem of the 3d Datum Transformation and the Procrustes Algorithm21 December 2011 Cross Ref The Sixth Problem of Generalized Algebraic Regression21 December 2011 Cross Ref Special Problems of Algebraic Regression and Stochastic Estimation21 December 2011 Cross Ref Algebraic Solutions of Systems of Equations21 December 2011 Cross Ref The First Problem of Probabilistic Regression: The Bias Problem21 December 2011 Cross Ref The Second Problem of Algebraic Regression21 December 2011 Cross Ref The Second Problem of Probabilistic Regression21 December 2011 Cross Ref The Third Problem of Algebraic Regression21 December 2011 Cross Ref The Third Problem of Probabilistic Regression21 December 2011 Cross Ref The Fourth Problem of Probabilistic Regression21 December 2011 Cross Ref The Fifth Problem of Algebraic Regression: The System of Conditional Equations: Homogeneous and Inhomogeneous Equations: $$\{\mathbf{By} = \mathbf{Bi}\ \mathbf{versus} -\mathbf{c} + \mathbf{By} = \mathbf{Bi}\}$$21 December 2011 Cross Ref Positive real and bounded real balancing for model reduction of descriptor systems14 September 2009 | International Journal of Control, Vol. 83, No. 1 Cross Ref Optimal multisensor data fusion for linear systems with missing measurements Cross Ref Generalized inverses of an invertible infinite matrix over a finite fieldLinear Algebra and its Applications, Vol. 418, No. 2-3 Cross Ref Optimal Linear Estimation and Data FusionIEEE Transactions on Automatic Control, Vol. 51, No. 4 Cross Ref Modeling Test Responses by Multivariable Polynomials of Higher DegreesJiGuan G. Lin4 August 2006 | SIAM Journal on Scientific Computing, Vol. 28, No. 3AbstractPDF (415 KB)Norm of alias matrices for balanced fractional 2 factorial designs when interesting factorial effects are not aliased with effects not of interest in estimationJournal of Statistical Planning and Inference, Vol. 106, No. 1-2 Cross Ref Bibliography13 January 2010 Cross Ref Balanced fractional 3m factorial designs of resolution IVJournal of Statistical Planning and In