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矩阵方程AX-XB=C的显式解──纪念导师郭仲衡教授*

陈玉明 肖衡

陈玉明, 肖衡. 矩阵方程AX-XB=C的显式解──纪念导师郭仲衡教授*[J]. 应用数学和力学, 1995, 16(12): 1051-1059.
引用本文: 陈玉明, 肖衡. 矩阵方程AX-XB=C的显式解──纪念导师郭仲衡教授*[J]. 应用数学和力学, 1995, 16(12): 1051-1059.
Chen Yuming, Xiao Heng. The Expliclt solution of the Matrix Equation AX-XB=C──To the memory of Prof[J]. Applied Mathematics and Mechanics, 1995, 16(12): 1051-1059.
Citation: Chen Yuming, Xiao Heng. The Expliclt solution of the Matrix Equation AX-XB=C──To the memory of Prof[J]. Applied Mathematics and Mechanics, 1995, 16(12): 1051-1059.

矩阵方程AX-XB=C的显式解──纪念导师郭仲衡教授*

基金项目: * 国家自然科学基金

The Expliclt solution of the Matrix Equation AX-XB=C──To the memory of Prof

  • 摘要: 现有关于矩阵方程AX-XB=C的显式解的几乎所有结论都是在A与B无公共特征值的条件下获得的。本文利用特征投影给出了方程在AB均对称或反对称时一般解的显式形式。我们所得到的结果不仅适用于任何特征值重数情形,而且可以用来讨论该方程的一般情形。
  • [1] W.E.Roth,The equation AX-YH=C and AX-XB=C in matrices.Proc.Amer.Math.Soc.,97(1952),392-396.
    [2] S.Barnett and C.Storey,Soma applications of Liapunov matrix equations,J.Inst.Math.Appl.,4,1(1968).33-42.
    [3] A.Iameson,Solution of the equation AX+XB=C by inversion of an M×M or N×N matrix,SIAM J.Appl.Math.,16(1968).1020-1023.
    [4] P.Lancaster,Explicit solution of Imear matrix equations,SIAM Rev.,12(1970).544-566.
    [5] D.H.Carlson and B.N.Datta.The Liapunov matrix equaiton SA+A*S=S*B*BS Linear Algebra Appl.,28(1979).43-53.
    [6] Eurice de Souza and S.P.Bhattacharyya.Controllability.observability and the solution of AX-XB=C.Linear Algebra Appl.,39(1981).167-188.
    [7] T.E.Djaferis and S.K.Mitter.Algebraic methods for the study of some linear matrix equations.Linear Algebra Appl.,44(1982).125-142.
    [8] J.K.John Jones and C.Lew.Solutions of Liapunov matrix equation BX-XA=C.IEEE Trans.Automatic AC-27(1982)464-466.
    [9] 高维新.矩阵方程AX-XB-C的连分式解法.中国科学.A辑.(5)(1988).576-584
    [10] H.K.Wimmer,Linear matrix equaiton:the module theoretic approach,Lemear Algebia Appl.,120(1989).149-164.
    [11] Ma Er-chieh,A finite series solution of the matrix equation.AX-XB=C.SIAM J.Appl.,Math.,14(1966).490-495.
    [12] B.N.Dana and h.Dana.The matrix equation XA=ATX and an assocrated algonthm for solving the inertia and stability problems.Lmear Algebra Appl.,97(1987).103-119.
    [13] Guo Zhongheng,T.H.Lehman,Liang Haoyun and C-S.Man Twirl tensors and the tensor equation AX-XA=C.J.Elascity.27.2(1992).227-245.
    [14] C.D.Luehr and M.B.Ruhm,The synificance of projector operators in the spectral representation of symmetric second order tensors,Comput.Methods.Appl.Mech.Engre.84(1990).243-246.
    [15] Guo Zhongheng,Li Jianbo Xiao Heng and Chen Yuming,Intrinsic solution to the n-dimensional tensor equation Σr-1mUm-r×Ur-1=C.Comput.Methods Appl.Mech.Engrg.115(1994).359-364.
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出版历程
  • 收稿日期:  1995-02-28
  • 刊出日期:  1995-12-15

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