Conditions for Positive and Nonnegative Definiteness in Terms of Pseudoinverses

摘要

Previous article Next article Conditions for Positive and Nonnegative Definiteness in Terms of PseudoinversesArthur AlbertArthur Alberthttps://doi.org/10.1137/0117041PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Richard Bellman, Introduction to matrix analysis, McGraw-Hill Book Co., Inc., New York, 1960xx+328 MR0122820 0124.01001 Google Scholar[2] 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[3] 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[4] 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 Error Analysis of Multirate Leapfrog-Type Methods for Second-Order Semilinear OdesConstantin Carle and Marlis HochbruckSIAM Journal on Numerical Analysis, Vol. 60, No. 5 | 13 October 2022AbstractPDF (1129 KB)The truncated moment problem on the union of parallel linesLinear Algebra and its Applications, Vol. 649 | 1 Sep 2022 Cross Ref On the non-symmetric semidefinite Procrustes problemLinear Algebra and its Applications, Vol. 648 | 1 Sep 2022 Cross Ref Dynamic discrete-time portfolio selection for defined contribution pension funds with inflation riskJournal of Industrial & Management Optimization, Vol. 18, No. 1 | 1 Jan 2022 Cross Ref Stability and Functional Superconvergence of Narrow-Stencil Second-Derivative Generalized Summation-By-Parts DiscretizationsJournal of Scientific Computing, Vol. 90, No. 1 | 10 December 2021 Cross Ref Nesbitt and Shapiro cyclic sum inequalities for positive definite matricesAdvances in Operator Theory, Vol. 7, No. 1 | 16 November 2021 Cross Ref Inverse eigenvalue problems for discrete gyroscopic systemsInverse Problems in Science and Engineering, Vol. 29, No. 12 | 8 February 2021 Cross Ref Simultaneous approximation terms and functional accuracy for diffusion problems discretized with multidimensional summation-by-parts operatorsJournal of Computational Physics, Vol. 445 | 1 Nov 2021 Cross Ref An alternative approach for solving the quadratic matrix equation C∗X∗AXC+C∗X∗B+B∗XC+D=0Journal of Computational and Applied Mathematics, Vol. 203–204 | 1 Nov 2021 Cross Ref Robust PI Observer Design of the Welding Process Model2021 China Automation Congress (CAC) | 22 Oct 2021 Cross Ref Infinite horizon LQ Nash Games for SDEs with infinite jumpsAsian Journal of Control, Vol. 23, No. 5 | 21 July 2020 Cross Ref Minimal-norm static feedbacks using dissipative Hamiltonian matricesLinear Algebra and its Applications, Vol. 623 | 1 Aug 2021 Cross Ref Characterization of the dissipative mappings and their application to perturbations of dissipative‐Hamiltonian systemsNumerical Linear Algebra with Applications, Vol. 29 | 14 July 2021 Cross Ref Observer-based multiplicative passive control for a class of uncertain time-delay sampled-data system2021 IEEE 4th Advanced Information Management, Communicates, Electronic and Automation Control Conference (IMCEC) | 18 Jun 2021 Cross Ref The Truncated Hamburger Moment Problems with Gaps in the Index SetIntegral Equations and Operator Theory, Vol. 93, No. 3 | 30 April 2021 Cross Ref Non-fragile load frequency control of multi-area power system with energy storage system and wind power subject to circular pole constraintsSustainable Energy Technologies and Assessments, Vol. 45 | 1 Jun 2021 Cross Ref Matrices with positive semidefinite real partLinear and Multilinear Algebra, Vol. 69, No. 3 | 11 April 2019 Cross Ref Semidefinite relaxation for the total least squares problem with Tikhonov-like regularizationOptimization, Vol. 70, No. 2 | 10 January 2020 Cross Ref The common Re-nonnegative definite and