A Finite Series Solution of the Matrix Equation $AX - XB = C$

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Previous article Next article A Finite Series Solution of the Matrix Equation $AX - XB = C$Er-Chieh MaEr-Chieh Mahttps://doi.org/10.1137/0114043PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] E. C. Ma, Masters Thesis, A matrix analysis of beam gridworks, Ph.D. Dissertation, Kansas State University, Manhattan, 1962 Google Scholar[2] F. R. Gantmacher, Applications of the theory of matrices, Translated by J. L. Brenner, with the assistance of D. W. Bushaw and S. Evanusa, Interscience Publishers, Inc., New York, 1959ix+317 MR0107648 (21:6372b) 0085.01001 Google Scholar[3] C. C. Macduffee, The Theory of Matrices, Chelsea, New York, 1946 Google Scholar[4] J. J. Sylvester, Sur la solution du cas le plus général des équations linéaires en quantités binaires, c'est-à-dire en quaternions ou en matrices du second ordre, C. R. Acad. Sci. Paris, 22 (1884), 117–118 Google Scholar[5] M. Wedderburn, Note on the linear matrix equation, Proc. Edinburgh Math. Soc., 22 (1904), 49–53 CrossrefGoogle Scholar[6] D. E. Rutherford, On the solution of the matrix equation $AX+XB=C$, Nederl. Akad. Wetensch. Proc. Ser. A, 35 (1932), 53–59 0004.19502 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Solutions to the linear transpose matrix equations and their application in control4 October 2020 | Computational and Applied Mathematics, Vol. 39, No. 4 Cross Ref Solving the Operator Equation $$\varvec{AX-XB} \varvec{=C}$$ A X - X B = C with Closed $$\varvec{A}$$ A and $$\varvec{B}$$ B18 July 2018 | Integral Equations and Operator Theory, Vol. 90, No. 5 Cross Ref The Vectorial Ribaucour Transformation for Submanifolds of Constant Sectional Curvature5 July 2017 | The Journal of Geometric Analysis, Vol. 28, No. 3 Cross Ref Spectral decomposition based solutions to the matrix equation1 January 2018 | IET Control Theory & Applications, Vol. 12, No. 1 Cross Ref Two-sided bounds on some output-related quantities in linear stochastically excited vibration systems with application of the differential calculus of norms2 March 2016 | Cogent Mathematics, Vol. 3, No. 1 Cross Ref Two-sided bounds on the mean vector and covariance matrix in linear stochastically excited vibration systems with application of the differential calculus of norms20 March 2015 | Cogent Mathematics, Vol. 2, No. 1 Cross Ref References9 June 2015 Cross Ref Matrix theory of wave propagation in hybrid electric/magnetic multiwire transmission line systems8 April 2015 | Journal of Electromagnetic Waves and Applications, Vol. 29, No. 7 Cross Ref On the vibration-suppression property and monotonicity behavior of a special weighted norm for dynamical systemsApplied Mathematics and Computation, Vol. 222 Cross Ref Explicit solutions to the matrix equation EXF − AX = C1 August 2013 | IET Control Theory & Applications, Vol. 7, No. 12 Cross Ref Closed-form solutions to Sylvester-conjugate matrix equationsComputers & Mathematics with Applications, Vol. 60, No. 1 Cross Ref On matrix equations X−AXF=C and X−AX¯F=CJournal of Computational and Applied Mathematics, Vol. 230, No. 2 Cross Ref Solution of the matrix eigenvalue problem VA+A*V=μV with applications to the study of free linear dynamical systemsJournal of Computational and Applied Mathematics, Vol. 213, No. 1 Cross Ref Kronecker Maps and Sylvester-Polynomial Matrix EquationsIEEE Transactions on Automatic Control, Vol. 52, No. 5 Cross Ref On solutions of the matrix equations XF−AX=C andApplied Mathematics and Computation, Vol. 183, No. 2 Cross Ref Bibliography Cross Ref On the numerical solution ofAX −XB =CBIT Numerical Mathematics, Vol. 36, No. 4 Cross Ref Principal axis intrinsic method and the high dimensional tensor equation AX?XA=CApplied Mathematics and Mechanics, Vol. 17, No. 10 Cross Ref The linear bi-spatial tensor equation ?i j AiXBj= CApplied Mathematics and Mechanics, Vol. 17, No. 10 Cross Ref The explicit solution of the matrix equation AX−XB=CApplied Mathematics and Mechanics, Vol. 16, No. 12 Cross Ref Chapter Two Continuous algebraic Lyapunov equation Cross Ref Chapter One Introduction Cross Ref A matrix equation approach to solving recurrence relations in two-dimensional random walks14 July 2016 | Journal of Applied Probability, Vol. 31, No. 03 Cross Ref A matrix equation approach to solving recurrence relations in two-dimensional random walks14 July 2016 | Journal of Applied Probability, Vol. 31, No. 3 Cross Ref Twirl tensors and the tensor equation AX−XA=CJournal of Elasticity, Vol. 27, No. 3 Cross Ref Explicit solution of the matrix equation AXB − CXD = ELinear Algebra and its Applications, Vol. 121 Cross Ref Controllability, observability and the solution of AX - XB = CLinear Algebra and its Applications, Vol. 39 Cross Ref The solution of the matrix equation XC – BX = D as an eigenvalue problemInternational Journal of Systems Science, Vol. 8, No. 4 Cross Ref $AX - XB = C$, Resultants and Generalized InversesRobert E. 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Smith12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 16, No. 1AbstractPDF (314 KB)On the general functional matrix for a linear systemIEEE Transactions on Automatic Control, Vol. 12, No. 4 Cross Ref Volume 14, Issue 3| 1966SIAM Journal on Applied Mathematics History Submitted:16 September 1965Published online:28 July 2006 InformationCopyright © 1966 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0114043Article page range:pp. 490-495ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics