The Pseudoinverse of a Rectangular or Singular Matrix and Its Application to the Solution of Systems of Linear Equations

Abstract

Previous article Next article The Pseudoinverse of a Rectangular or Singular Matrix and Its Application to the Solution of Systems of Linear EquationsT. N. E. GrevilleT. N. E. Grevillehttps://doi.org/10.1137/1001003PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc., 51 (1955), 406–413 MR0069793 0065.24603 CrossrefGoogle Scholar[2] R. Penrose, On best approximation solutions of linear matrix equations, Proc. Cambridge Philos. Soc., 52 (1956), 17–19 MR0074092 0070.12501 CrossrefGoogle Scholar[3] Arne Bjerhammar, Application of calculus of matrices to method of least squares with special reference to geodetic calculations, Trans. Roy. Inst. Tech. Stockholm, 1951 (1951), 86 pp. (2 plates) MR0055793 Google Scholar[4] Arne Bjerhammar, Rectangular reciprocal matrices, with special reference to geodetic calculations, Bull. Géodésique, 1951 (1951), 188–220 MR0043758 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails H∞ -PID distributed control for output leader-tracking and containment of heterogeneous MASs with external disturbancesJournal of Control and Decision, Vol. 9, No. 4 | 24 December 2021 Cross Ref Improving MRAC Transient Response Using Generalized Dynamic Inversion and Nullspace ParametrizationIFAC-PapersOnLine, Vol. 55, No. 12 | 1 Jan 2022 Cross Ref Successive Generalized Dynamic Inversion Control of Lateral Fighter Aircraft Dynamics*2021 9th International Conference on Systems and Control (ICSC) | 24 Nov 2021 Cross Ref Experimental noise source identification in a fuselage test environment based on nearfield acoustical holographyCEAS Aeronautical Journal, Vol. 12, No. 4 | 18 August 2021 Cross Ref A Model-free Deep Reinforcement Learning Approach for Robotic Manipulators Path Planning2021 21st International Conference on Control, Automation and Systems (ICCAS) | 12 Oct 2021 Cross Ref Some additive results on M-P inverse of operator productAsian-European Journal of Mathematics, Vol. 14, No. 01 | 18 October 2019 Cross Ref An optimal distributed PID-like control for the output containment and leader-following of heterogeneous high-order multi-agent systemsInformation Sciences, Vol. 541 | 1 Dec 2020 Cross Ref Mutual Direct State Controllability Analysis of Multivariable Underactuated LTI Systems2020 Australian and New Zealand Control Conference (ANZCC) | 26 Nov 2020 Cross Ref Using prior parameter knowledge in model‐based design of experiments for pharmaceutical productionAIChE Journal, Vol. 66, No. 11 | 26 August 2020 Cross Ref Mutual Direct Controllability of MIMO Systems and Application to Longitudinal Aircraft Control2020 24th International Conference on System Theory, Control and Computing (ICSTCC) | 8 Oct 2020 Cross Ref Neural Network-based Hybrid Position/Force Tracking Control for Flexible Joint Robot2020 IEEE International Systems Conference (SysCon) | 24 Aug 2020 Cross Ref Femtosecond-resolved observation of the fragmentation of buckminsterfullerene following X-ray multiphoton ionizationNature Physics, Vol. 15, No. 12 | 23 September 2019 Cross Ref Canonical Kane's Equations of Motion for Discrete Dynamical SystemsAIAA Journal, Vol. 57, No. 10 | 1 Oct 2019 Cross Ref Sequential model-based A- and V-optimal design of experiments for building fundamental models of pharmaceutical production processesComputers & Chemical Engineering, Vol. 129 | 1 Oct 2019 Cross Ref Quadrotor Control Via Robust Generalized Dynamic Inversion and Adaptive Non‐Singular Terminal Sliding ModeAsian Journal of Control, Vol. 21, No. 3 | 30 April 2018 Cross Ref Development and experimental investigation of a Quadrotor's robust generalized dynamic inversion control systemNonlinear Dynamics, Vol. 96, No. 2 | 8 March 2019 Cross Ref Sequential Model-Based A-Optimal Design of Experiments When the Fisher Information Matrix Is NoninvertibleIndustrial & Engineering Chemistry Research, Vol. 58, No. 3 | 20 December 2018 Cross Ref Passing Through Jacobian Singularities in Motion Path Control of Redundant Robot ArmsAdvances in Service and Industrial Robotics | 29 September 2018 Cross Ref Optimization of Model Operator for Service Robot, Intended to Service Persons with DisabilityIFAC-PapersOnLine, Vol. 52, No. 25 | 1 Jan 2019 Cross Ref Positional control of rotary servo cart system using generalized dynamic inversionJournal of Vibroengineering, Vol. 20, No. 6 | 30 September 2018 Cross Ref Canonical Generalized Inversion Form of Kane's Equations of Motion for Constrained Mechanical SystemsNonlinear Systems - Modeling, Estimation, and Stability | 18 July 2018 Cross Ref Kernel-Based Multilayer Extreme Learning Machines for Representation LearningIEEE Transactions on Neural Networks and Learning Systems, Vol. 29, No. 3 | 1 Mar 2018 Cross Ref Methods Based on Models for Domain KnowledgeStatistical Data Cleaning with Applications in R | 23 February 2018 Cross Ref ReferencesStatistical Data Cleaning with Applications in R | 23 February 2018 Cross Ref Generalized Inversion Form of Kane's Equations of Motion for Constrained Dynamical Systems2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference | 7 January 2018 Cross Ref Redundant Robotic Manipulator Path Planning for Real-Time Obstacle and Self-Collision AvoidanceAdvances in Service and Industrial Robotics | 27 July 2017 Cross Ref Real-time distance query and collision avoidance for point clouds with heavy-duty redundant manipulator2017 IEEE International Conference on Cybernetics and Intelligent Systems (CIS) and IEEE Conference on Robotics, Automation and Mechatronics (RAM) | 1 Nov 2017 Cross Ref Robust Generalized Dynamic Inversion Quadrotor ControlIFAC-PapersOnLine, Vol. 50, No. 1 | 1 Jul 2017 Cross Ref MDictionary of Mathematical Geosciences | 30 May 2017 Cross Ref PDictionary of Mathematical Geosciences | 30 May 2017 Cross Ref GDictionary of Mathematical Geosciences | 30 May 2017 Cross Ref IDictionary of Mathematical Geosciences | 30 May 2017 Cross Ref Partial eigenstructure assignment on LQR control for continuous LTI systems2016 4th International Conference on Control Engineering & Information Technology (CEIT) | 1 Dec 2016 Cross Ref Damage Assessment Algorithms for Structural Health MonitoringStructural Health Monitoring Technologies and Next-Generation Smart Composite Structures | 30 January 2017 Cross Ref COHERENT NETWORK ANALYSIS FOR CONTINUOUS GRAVITATIONAL WAVE SIGNALS IN A PULSAR TIMING ARRAY: PULSAR PHASES AS EXTRINSIC PARAMETERSThe Astrophysical Journal, Vol. 815, No. 2 | 17 December 2015 Cross Ref A Fuzzy Logic to Solve the Robotic Inverse Kinematic ProblemApplied Mechanics and Materials, Vol. 772 | 1 July 2015 Cross Ref Verification of Linear (In)Dependence in Finite Precision ArithmeticMathematics in Computer Science, Vol. 8, No. 3-4 | 25 July 2014 Cross Ref The Backus-Gilbert method and their minimum-norm solutionGEOPHYSICS, Vol. 78, No. 3 | 1 May 2013 Cross Ref Aircraft multi-constrainedgeneralized dynamic inversion control2013 9th International Symposium on Mechatronics and its Applications (ISMA) | 1 Apr 2013 Cross Ref An empirical model of erythemal ultraviolet radiation in the city of Valencia, SpainPhotochemical & Photobiological Sciences, Vol. 12, No. 9 | 1 Jan 2013 Cross Ref Improved MR phase-contrast velocimetry using a novel nine-point balanced motion-encoding scheme with increased robustness to eddy current effectsMagnetic Resonance in Medicine, Vol. 69, No. 1 | 5 March 2012 Cross Ref Guaranteeing task prioritization for redundant robots given maximum number of tasks and singularitiesTENCON 2012 IEEE Region 10 Conference | 1 Nov 2012 Cross Ref Aircraft Multi-Constrained Generalized Dynamic Inversion ControlIFAC Proceedings Volumes, Vol. 45, No. 1 | 1 Jan 2012 Cross Ref Inertia-independent generalized dynamic inversion feedback control of spacecraft attitude maneuversActa Astronautica, Vol. 68, No. 11-12 | 1 Jun 2011 Cross Ref Inertia-independent generalized dynamic inversion feedback control of spacecraft attitude maneuversProceedings of 5th International Conference on Recent Advances in Space Technologies - RAST2011 | 1 Jun 2011 Cross Ref Contour Tracking of a Redundant Robot Using Integral Variable Structure Control with Output FeedbackJournal of Intelligent & Robotic Systems, Vol. 62, No. 2 | 2 September 2010 Cross Ref Note on the weighted generalized inverse of the product of matricesJournal of Applied Mathematics and Computing, Vol. 35, No. 1-2 | 29 December 2009 Cross Ref Inertia-Independent Generalized Dynamic Inversion Spacecraft ControlIFAC Proceedings Volumes, Vol. 44, No. 1 | 1 Jan 2011 Cross Ref Aircraft maneuvering control using generalized dynamic inversion and semidefinite Lyapunov functions2010 IEEE International Conference on Control Applications | 1 Sep 2010 Cross Ref Hybrid motion planning of a planar robot for a tracking problem with singularity2010 8th IEEE International Conference on Industrial Informatics | 1 Jul 2010 Cross Ref Globally asymptotic generalized dynamic inversion for robot manipulator control design18th Mediterranean Conference on Control and Automation, MED'10 | 1 Jun 2010 Cross Ref Spacecraft generalized dynamic inversion attitude control18th Mediterranean Conference on Control and Automation, MED'10 | 1 Jun 2010 Cross Ref Asymptotic generalised dynamic inversion attitude controlIET Control Theory & Applications, Vol. 4, No. 5 | 1 May 2010 Cross Ref An analytical model for dispersion of pollutants from a continuous source in the atmospheric boundary layerProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 466, No. 2114 | 21 October 2009 Cross Ref Servo-constraint generalized inverse dynamics for robot manipulator control design2009 IEEE International Conference on Control and Automation | 1 Dec 2009 Cross Ref Asymptotic perturbed feedback linearisation of underactuated Euler's dynamicsInternational Journal of Control, Vol. 82, No. 10 | 6 August 2009 Cross Ref Generalised dynamic inversion spacecraft control design methodologiesIET Control Theory & Applications, Vol. 3, No. 2 | 1 Feb 2009 Cross Ref Singularly perturbed feedback linearization with linear attitude deviation dynamics realizationNonlinear Dynamics, Vol. 53, No. 4 | 11 December 2007 Cross Ref Perturbed feedback linearization of attitude dynamics2008 American Control Conference | 1 Jun 2008 Cross Ref Controls coefficient generalized inversion Lyapunov design for spacecraft attitude control2008 IEEE International Conference on Control Applications | 1 Jan 2008 Cross Ref Experiments on orthogonalization by biorthogonal representations of orthogonal projectorsJournal of Computational and Applied Mathematics, Vol. 205, No. 1 | 1 Aug 2007 Cross Ref Greedy Basis PursuitIEEE Transactions on Signal Processing, Vol. 55, No. 7 | 1 Jul 2007 Cross Ref Constructive updating/downdating of oblique projectors: a generalization of the Gram–Schmidt processJournal of Physics A: Mathematical and Theoretical, Vol. 40, No. 24 | 30 May 2007 Cross Ref Rank deficiency and Tikhonov regularization in the inverse problem for gravitational-wave burstsClassical and Quantum Gravity, Vol. 23, No. 19 | 15 September 2006 Cross Ref An alternative proof for the recursive formulae for computing the Moore–Penrose M-inverse of a matrixApplied Mathematics and Computation, Vol. 174, No. 1 | 1 Mar 2006 Cross Ref Modeling Test Responses by Multivariable Polynomials of Higher DegreesJiGuan G. LinSIAM Journal on Scientific Computing, Vol. 28, No. 3 | 4 August 2006AbstractPDF (415 KB)Complexity: What, Why, and HowComputational Error and Complexity in Science and Engineering | 1 Jan 2005 Cross Ref NEW RECURSIVE LEAST SQUARE ALGORITHMS WITHOUT USING THE INITIAL INFORMATIONIFAC Proceedings Volumes, Vol. 38, No. 1 | 1 Jan 2005 Cross Ref Simulating a Robotic Arm in a Box: Redundant Kinematics, Path Planning, and Rapid Prototyping for Enclosed SpacesSIMULATION, Vol. 80, No. 6 | 18 August 2016 Cross Ref Optimal State Estimation With Failed Sensor Discrimination and IdentificationJournal of Guidance, Control, and Dynamics, Vol. 27, No. 3 | 1 May 2004 Cross Ref Motion planning of redundant robots by perturbation methodMechatronics, Vol. 14, No. 3 | 1 Apr 2004 Cross Ref Mathematics for modal analysisModal Analysis | 1 Jan 2001 Cross Ref Human Modeling: Inverse Kinematics with Maximum Joint AvailabilityProceedings of the Human Factors and Ergonomics Society Annual Meeting, Vol. 44, No. 38 | 5 November 2016 Cross Ref O(n3) noniterative heuristic algorithm for linear programs with error-free implementationApplied Mathematics and Computation, Vol. 110, No. 1 | 1 Apr 2000 Cross Ref A direct heuristic algorithm for linear programmingProceedings Mathematical Sciences, Vol. 110, No. 1 | 1 Feb 2000 Cross Ref Solving linear differential equations as a minimum norm least squares problem with error-boundsInternational Journal of Computer Mathematics, Vol. 74, No. 3 | 1 Jan 2000 Cross Ref Solving linear programming problems exactlyApplied Mathematics and Computation, Vol. 81, No. 1 | 1 Jan 1997 Cross Ref Fuzzy parameter identification of direct drive robotsJournal of the Franklin Institute, Vol. 333, No. 2 | 1 Mar 1996 Cross Ref Multidimensional Inverse Problems in Ultrasonic ImagingMultidimensional Systems: Signal Processing and Modeling Techniques | 1 Jan 1995 Cross Ref Common Misconceptions about Neural Networks as ApproximatorsJournal of Computing in Civil Engineering, Vol. 8, No. 3 | 1 Jul 1994 Cross Ref Concise row-pruning algorithm to invert a matrixApplied Mathematics and Computation, Vol. 61, No. 1 | 1 Mar 1994 Cross Ref Large Least Squares Problems Involving Kronecker ProductsDonald W. Fausett and Charles T. FultonSIAM Journal on Matrix Analysis and Applications, Vol. 15, No. 1 | 31 July 2006AbstractPDF (881 KB)ON SYSTOLIC GENERAL SYSTEM SOLUTION AND GENERAL MATRIX INVERSIONParallel Algorithms and Applications, Vol. 3, No. 3-4 | 1 Jan 1994 Cross Ref Hybrid Position/Force Control: A Correct FormulationThe International Journal of Robotics Research, Vol. 11, No. 4 | 2 July 2016 Cross Ref A learning and forgetting algorithm in associative memories: results involving pseudo-inversesIEEE Transactions on Circuits and Systems, Vol. 38, No. 10 | 1 Oct 1991 Cross Ref Ideal state reconstructor for deterministic digital control systemsInternational Journal of Control, Vol. 49, No. 6 | 1 Jun 1989 Cross Ref An Investigation of Frictionless Enveloping Grasping in the PlaneThe International Journal of Robotics Research, Vol. 7, No. 3 | 2 July 2016 Cross Ref An iterative pipelined array architecture for the generalized matrix inversionInformation Processing Letters, Vol. 26, No. 5 | 1 Jan 1988 Cross Ref An optimum approximation for residual stiffness in linear system identification28th Structures, Structural Dynamics and Materials Conference | 17 August 2012 Cross Ref On linear output feedback controlIEEE Transactions on Circuits and Systems, Vol. 33, No. 4 | 1 Apr 1986 Cross Ref Obstacle Avoidance for Kinematically Redundant Manipulators in Dynamically Varying EnvironmentsThe International Journal of Robotics Research, Vol. 4, No. 3 | 2 July 2016 Cross Ref Computational modeling for the computer animation of legged figuresACM SIGGRAPH Computer Graphics, Vol. 19, No. 3 | 1 Jul 1985 Cross Ref SAM-animation software for simulating articulated motionComputers & Graphics, Vol. 9, No. 4 | 1 Jan 1985 Cross Ref The fuel property/flame radiation relationship for gas turbine combustorsAIAA Journal, Vol. 22, No. 12 | 1 Dec 1984 Cross Ref Application of the generalized inverse in structural system identificationAIAA Journal, Vol. 22, No. 12 | 1 Dec 1984 Cross Ref Model reduction for linear multivariable systemsIEEE Transactions on Automatic Control, Vol. 25, No. 6 | 1 Dec 1980 Cross Ref Dynamic Structural Identification Tasks and MethodsCIRP Annals, Vol. 29, No. 1 | 1 Jan 1980 Cross Ref On the predictive power of the new approach to consumer theoryAtlantic Economic Journal, Vol. 7, No. 2 | 1 Jul 1979 Cross Ref EXTRAPOLATING TO THE LIMIT OF A VECTOR SEQUENCE11This research was carried out under the Mathematical Sciences Research Program, Task Area SR0140301 (Math Sciences), supported by the Naval Sea Systems Command.Information Linkage Between Applied Mathematics and Industry | 1 Jan 1979 Cross Ref Identification of Lumped Element Models from Response Measurements of Vibrating StructuresDynamics of Multibody Systems | 1 Jan 1978 Cross Ref A New Weighted Generalized Inverse Algorithm for Pattern RecognitionIEEE Transactions on Computers, Vol. C-26, No. 10 | 1 Oct 1977 Cross Ref Conjugate-gradient method for computing the Moore-Penrose inverse and rank of a matrixJournal of Optimization Theory and Applications, Vol. 22, No. 1 | 1 May 1977 Cross Ref Viking satellite orbit determination15th Aerospace Sciences Meeting | 16 August 2012 Cross Ref An introduction to nonlinear programming—IV Numerical methods for constrained minimizationComputers & Electrical Engineering, Vol. 3, No. 4 | 1 Dec 1976 Cross Ref A simple method for finding a basis for the null-space of a matrixIEEE Transactions on Automatic Control, Vol. 21, No. 3 | 1 Jun 1976 Cross Ref Algebraic Aspects of the Generalized Inverse of a Rectangular MatrixGeneralized Inverses and Applications | 1 Jan 1976 Cross Ref Annotated Bibliography on Generalized Inverses and ApplicationsGeneralized Inverses and Applications | 1 Jan 1976 Cross Ref Convergence bounds for nonlinear programming algorithmsMathematical Programming, Vol. 8, No. 1 | 1 Dec 1975 Cross Ref Mach Reflection Using Ray-Shock TheoryAIAA Journal, Vol. 13, No. 11 | 1 Nov 1975 Cross Ref Practical Aspect of the Generalized Inverse of a MatrixAIAA Journal, Vol. 13, No. 11 | 1 Nov 1975 Cross Ref Crime statistics: A mathematical perspectiveJournal of Criminal Justice, Vol. 3, No. 3 | 1 Sep 1975 Cross Ref Multivariable system design by transfer function synthesisInternational Journal of Systems Science, Vol. 6, No. 9 | 1 Sep 1975 Cross Ref Pole assignment techniques for multivariable systems using unity rank output feedbackInternational Journal of Control, Vol. 21, No. 6 | 1 Jun 1975 Cross Ref THE GENERALIZED INVERSE, WITH NONLINEAR REGRESSION AND MATHEMATICAL PROGRAMMING APPLICATIONSDecision Sciences, Vol. 6, No. 2 | 1 Apr 1975 Cross Ref ON-line-ridge regression; sequential biased estimation for nonorthogonai problemsJournal of Statistical Computation and Simulation, Vol. 3, No. 3 | 1 Jan 1975 Cross Ref Control of a binary distillation column utilizing a simple control lawThe Canadian Journal of Chemical Engineering, Vol. 52, No. 6 | 1 Dec 1974 Cross Ref MODEL REFERENCE ADAPTIVE CONTROL BASED ON LIAPUNOV'S DIRECT METHOD Part I: Theory and Control System Design†Chemical Engineering Communications, Vol. 1, No. 3 | 21 May 2007 Cross Ref Geometric Programming: A Technical State-of-the-Art SurveyA I I E Transactions, Vol. 5, No. 2 | 9 July 2007 Cross Ref Approximation of discrete linear systemsInternational Journal of Control, Vol. 17, No. 3 | 27 March 2007 Cross Ref Optimal Observer Techniques for Linear Discrete Time Systems1 1This research was supported in part by the Air Force office of Scientific Research under AFOSR Grant 72–2166.Control and Dynamic Systems | 1 Jan 1973 Cross Ref The product of operators with closed rangeTohoku Mathematical Journal, Vol. 25, No. 3 | 1 Jan 1973 Cross Ref Reduction and transformation of linear discrete-time-varying systems†International Journal of Control, Vol. 16, No. 6 | 1 Dec 1972 Cross Ref A Partial-Step Algorithm for the Nonlinear Estimation ProblemAIAA Journal, Vol. 10, No. 5 | 1 May 1972 Cross Ref The Invariance Properties of a Multivalue n-Port in a Linear EmbeddingIEEE Transactions on Circuit Theory, Vol. 19, No. 2 | 1 Mar 1972 Cross Ref ReferencesRegression and the Moore-Penrose Pseudoinverse | 1 Jan 1972 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 A method for nonlinear Programming, Vol. 1, No. 1 | 1 Dec Cross Ref Theory of Models of Dynamic Journal, Vol. 9, No. 8 | 1 Aug Cross Ref Generalized and for Singular Operator Analysis and Applications | 1 Jan Cross Ref FOR A WITHOUT Methods in | 1 Jan Cross Ref A Applied to Transactions on Engineering, Vol. No. 1 | 1 Jan Cross Ref An of the Generalized Inverse of a E. and T. N. E. Journal on Applied Mathematics, Vol. 19, No. 4 | 12 July 2006AbstractPDF Note on the Generalized Inverses of Some R. and Journal on Applied Mathematics, Vol. 19, No. 3 | 12 July 2006AbstractPDF Linear Estimation, and Nonlinear Vol. 12, No. 3 | 1 Aug Cross Ref A Pseudoinverse and Its Application to Constrained and Journal on Applied Mathematics, Vol. 19, No. 1 | 12 July 2006AbstractPDF Note on the Solution of Rectangular Linear Systems by N. Vol. 12, No. 3 | 18 July 2006AbstractPDF of a system for using output Transactions on Automatic Control, Vol. 15, No. 3 | 1 Jun Cross Ref Time design of recursive digital Transactions on and Vol. No. 2 | 1 Jun Cross Ref THE OF OF Structures, Structural Dynamics, and Materials Conference | 16 August 2012 Cross Ref articulated and control in Computer Cross Ref Solution of the inverse problem of a manipulator by a IEEE International Conference on Fuzzy Cross Ref A Hybrid of the International Conference on Intelligent and Systems Cross Ref and experimental results of based planning for of International Conference on Intelligent and Systems Cross Ref of redundant manipulator constrained of IEEE International Conference on Robotics and Automation Cross Ref with Computer for Linear Circuit Transactions on Vol. 12, No. 3 | 1 Sep Cross Ref Some of Vol. No. 1 | 1 Mar Cross Ref Vol. 3, No. | 4 May 2009 Cross Ref Das verallgemeinerte Inverse für die reine und angewandte Mathematik (Crelles Journal), Vol. No. | 1 Jan Cross Ref and of the algorithm for linear least squares of Computation, Vol. 23, No. | 1 January Cross Ref A on generalized Research Vol. 15, No. 4 | 29 October 2013 Cross Ref Generalized Inverse Approach to Adaptive Pattern Transactions on Computers, Vol. No. 12 | 1 Dec Cross Ref of and T. G. Journal on Applied Mathematics, Vol. 16, No. 4 | 12 July 2006AbstractPDF OF Research, Vol. 3, No. 3 | 1 Jul Cross Ref A transformation model for Vol. No. 1-2 | 1 Jan Cross Ref A Note on Generalized and the Journal on Numerical Vol. 4, No. 4 | July 2006AbstractPDF Computing the of of the Vol. 14, No. 4 | 1 Oct Cross Ref On generalized and on the of with to iterative of Mathematical Analysis and Applications, Vol. No. 3 | 1 Jun Cross Ref On the of or of the American Statistical Vol. 62, No. | 1 Jun Cross Ref Measurements of a Vol. 9, No. 2 | 18 July 2006AbstractPDF of Sequential Linear Transactions on Aerospace and Systems, Vol. No. 2 | 1 Mar Cross Ref On the matrix of Mathematical Analysis and Applications, Vol. 17, No. 1 | 1 Jan Cross Ref Time weighted control of control systemsIEEE Transactions on Automatic Control, Vol. 11, No. 4 | 1 Oct Cross Ref On Computation of Generalized Inverses and and Journal on Numerical Vol. 3, No. 3 | July 2006AbstractPDF the to the Generalized Inverse of Matrix of the Vol. 13, No. 3 | 1 Jul Cross Ref State for digital controlIEEE Transactions on Automatic Control, Vol. 11, No. 2 | 1 Apr Cross Ref Generalized Inverses and Generalized Journal on Applied Mathematics, Vol. 14, No. 2 | July 2006AbstractPDF Partial in Journal on Applied Mathematics, Vol. 14, No. 3 | July 2006AbstractPDF for the Generalized Inverse of of E. of the Society for Industrial and Applied Mathematics Numerical Vol. No. 1 | 3 August 2006AbstractPDF Least Squares of Linear E. of the Society for Industrial and Applied Mathematics Numerical Vol. No. 2 | July 2006AbstractPDF and of with Singular of the American Statistical Vol. No. | 1 Dec Cross Ref for the Generalized Inverse of a E. of the Society for Industrial and Applied Mathematics, Vol. 12, No. 3 | July 2006AbstractPDF Matrix Pseudoinverse and Vol. 6, No. 2 | 18 July 2006AbstractPDF on the Generalized Inverse of the of E. Vol. 6, No. 1 | 18 July to the Theory of Generalized and of the Society for Industrial and Applied Mathematics, Vol. 11, No. 3 | July 2006AbstractPDF Note on and of the Society for Industrial and Applied Mathematics, Vol. 11, No. 2 | July 2006AbstractPDF Application of the Theory to Matrix of the Society for Industrial and Applied Mathematics, Vol. 9, No. 3 | 10 July 2006AbstractPDF on of of N. E. of the Society for Industrial and Applied Mathematics, Vol. 9, No. 1 | 10 July 2006AbstractPDF Applications of the Pseudoinverse of a N. E. Vol. No. 1 | 18 July 2006AbstractPDF 1, July 2006 Society for Industrial and Applied & for Industrial and Applied Mathematics