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 |