A Generalized Inverse Which Gives all the Integral Solutions to a System of Linear Equations

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Previous article Next article A Generalized Inverse Which Gives all the Integral Solutions to a System of Linear EquationsMichiel F. Hurt and Carter WaidMichiel F. Hurt and Carter Waidhttps://doi.org/10.1137/0119053PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Burton W. Jones, The Arithmetic Theory of Quadratic Forms, Carcus Monograph Series, no. 10, The Mathematical Association of America, Buffalo, N. Y., 1950, 61–62 MR0037321 0041.17505 Google Scholar[2] Irving Kaplansky, Elementary divisors and modules, Trans. Amer. Math. Soc., 66 (1949), 464–491 MR0031470 0036.01903 CrossrefISIGoogle Scholar[3] Marvin Marcus and , Henryk Minc, A survey of matrix theory and matrix inequalities, Allyn and Bacon Inc., Boston, Mass., 1964xvi+180 MR0162808 0126.02404 Google Scholar[4] R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc., 51 (1955), 406–413 MR0069793 0065.24603 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Channel Estimation and Self-Positioning for UAV SwarmIEEE Transactions on Communications, Vol. 67, No. 11 | 1 Nov 2019 Cross Ref Solution of Systems of Linear Diophantine EquationsComputer Algebra in Scientific Computing CASC 2001 | 1 Jan 2001 Cross Ref Applications of Generalized InversesSystems and Management Science by Extremal Methods | 1 Jan 1992 Cross Ref An application of the Hermite normal form in integer programmingLinear Algebra and its Applications, Vol. 140 | 1 Oct 1990 Cross Ref On an integral transformation for integer programmingOperations Research Letters, Vol. 7, No. 4 | 1 Aug 1988 Cross Ref Generalized inverses of matrices: a perspective of the work of PenroseMathematical Proceedings of the Cambridge Philosophical Society, Vol. 100, No. 3 | 24 October 2008 Cross Ref A computational form for finding the integral solutions to a system of linear equationsComputers & Mathematics with Applications, Vol. 7, No. 5 | 1 Jan 1981 Cross Ref Nonnegative integral solution of linear equationsProceedings of the Indian Academy of Sciences - Section A, Vol. 89, No. 1 | 1 Jan 1980 Cross Ref An introduction to the application of the simplest matrix-generalized inverse in systems scienceIEEE Transactions on Circuits and Systems, Vol. 25, No. 9 | 1 Sep 1978 Cross Ref An integer arithmetic method to compute generalized matrix inverse and solve linear equations exactlyProceedings of the Indian Academy of Sciences - Section A, Vol. 87, No. 9 | 1 Sep 1978 Cross Ref Further results on integral generalized inverses of integral matricesLinear and Multilinear Algebra, Vol. 6, No. 3 | 30 May 2007 Cross Ref Finite field computation technique for exact solution of systems of linear equations and interval linear programming problemsInternational Journal of Systems Science, Vol. 8, No. 10 | 30 March 2007 Cross Ref Annotated Bibliography on Generalized Inverses and ApplicationsGeneralized Inverses and Applications | 1 Jan 1976 Cross Ref Applications of Generalized Inverses to Programming, Games and NetworksGeneralized Inverses and Applications | 1 Jan 1976 Cross Ref $AX - XB = C$, Resultants and Generalized InversesRobert E. HartwigSIAM Journal on Applied Mathematics, Vol. 28, No. 1 | 12 July 2006AbstractPDF (1879 KB)On the General Solution to Systems of Mixed-Integer Linear EquationsV. J. Bowman and Claude-Alain BurdetSIAM Journal on Applied Mathematics, Vol. 26, No. 1 | 12 July 2006AbstractPDF (400 KB) Volume 19, Issue 3| 1970SIAM Journal on Applied Mathematics History Submitted:16 December 1969Published online:12 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0119053Article page range:pp. 547-550ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics