Explicit Solutions of Linear Matrix Equations

Abstract

Previous article Next article Explicit Solutions of Linear Matrix EquationsPeter LancasterPeter Lancasterhttps://doi.org/10.1137/1012104PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] N. Dunford and , J. T. Schwarz, Linear Operators, Part I, Interscience, New York, 1966 Google Scholar[2] F. R. Gantmacher, The theory of matrices. Vol. 1, Translated by K. A. Hirsch, Chelsea Publishing Co., New York, 1959x+374 MR0107649 Google Scholar[3] W. Givens, Elementary divisors and some properties of the Lyapunov mapping X→AX+XA*, Argonne National Laboratory, Illinois, 1961 Google Scholar[4] Erhard Heinz, Beiträge zur Störungstheorie der Spektralzerlegung, Math. Ann., 123 (1951), 415–438 10.1007/BF02054965 MR0044747 0043.32603 CrossrefGoogle Scholar[5] Alston S. Householder, The theory of matrices in numerical analysis, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1964xi+257 MR0175290 0161.12101 Google Scholar[6] Antony Jameson, Solution of the equation $AX+XB=C$ by inversion of an $M\times M$ or $N\times N$ matrix, SIAM J. Appl. Math., 16 (1968), 1020–1023 10.1137/0116083 MR0234974 0169.35202 LinkISIGoogle Scholar[7] M. G. Krein, Lectures on Stability Theory in the Solution of Differential Equations in a Banach Space, Inst. of Math., Ukrainian Acad. Sci., (1964), , (In Russian.) Google Scholar[8] Peter Lancaster, Theory of matrices, Academic Press, New York, 1969xii+316 MR0245579 0186.05301 Google Scholar[9] Er-chieh Ma, A finite series solution of the matrix equation $AX-XB=C$, SIAM J. Appl. Math., 14 (1966), 490–495 10.1137/0114043 MR0201456 0144.27003 LinkISIGoogle Scholar[10] C. C. MacDuffee, The Theory of Matrices, Chelsea, New York, 1956 Google Scholar[11] Alexander Ostrowski and , Hans Schneider, Some theorems on the inertia of general matrices, J. Math. Anal. Appl., 4 (1962), 72–84 10.1016/0022-247X(62)90030-6 MR0142555 0112.01401 CrossrefGoogle Scholar[12] Marvin Rosenblum, On the operator equation $BX-XA=Q$, Duke Math. J., 23 (1956), 263–269 10.1215/S0012-7094-56-02324-9 MR0079235 0073.33003 CrossrefISIGoogle Scholar[13] Marvin Rosenblum, The operator equation $BX-XA=Q$ with self-adjoint A and B, Proc. Amer. Math. Soc., 20 (1969), 115–120 MR0233214 0167.42801 ISIGoogle Scholar[14] William E. Roth, The equations $AX-YB=C$ and $AX-XB=C$ in matrices, Proc. Amer. Math. Soc., 3 (1952), 392–396 MR0047598 0047.01901 ISIGoogle Scholar[15] 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[16] R. A. Smith, Bounds for quadratic Lyapunov functions, J. Math. Anal. Appl., 12 (1965), 425–435 10.1016/0022-247X(65)90010-7 MR0190475 0135.29802 CrossrefISIGoogle Scholar[17] R. A. Smith, Matrix equation $XA+BX=C$, SIAM J. Appl. Math., 16 (1968), 198–201 10.1137/0116017 MR0224268 0157.22603 LinkISIGoogle Scholar[18] Anthony Trampus, A canonical basis for the matrix transformation $X\rightarrow AXB$, J. Math. Anal. Appl., 14 (1966), 153–160 10.1016/0022-247X(66)90068-0 MR0195875 0168.03201 CrossrefISIGoogle Scholar[19] Anthony Trampus, A canonical basis for the matrix transformation $X\rightarrow AX+XB$, J. Math. Anal. Appl, 14 (1966), 242–252 10.1016/0022-247X(66)90024-2 MR0190157 0145.25205 CrossrefISIGoogle Scholar[20] J. H. M. Wedderburn, Note on the linear matrix equation, Proc. Edinburgh Math. Soc., 22 (1904), 49–53 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails The dynamical functional particle method for multi-term linear matrix equationsApplied Mathematics and Computation, Vol. 435 | 1 Dec 2022 Cross Ref Lyapunov–Sylvester computational method for numerical solutions of a mixed cubic-superlinear Schrödinger systemEngineering with Computers, Vol. 38, No. S2 | 16 January 2021 Cross Ref Smoothness Regularized Multiview Subspace Clustering With Kernel LearningIEEE Transactions on Neural Networks and Learning Systems, Vol. 32, No. 11 | 1 Nov 2