矩阵方程<em>AX－XB＝C</em>的显式解──纪念导师郭仲衡教授<sup>*</sup>

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^*

陈玉明¹,
肖衡²

1.
湖南大学数学系长沙 410012;
2.
北京大学数学系北京 100871

基金项目: * 国家自然科学基金

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出版历程
- 收稿日期: 1995-02-28
- 刊出日期: 1995-12-15

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

Chen Yuming¹,
Xiao Heng²

1.
Department of Applied Mathematics, Human University, Changsha 410012, P. P. China;
2.
Departmeni of Mafhematics, Peking University, Beijing 100871, P. R. China

摘要

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A与B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。
- 矩阵方程 /
- 显式解 /
- 特征投影 /
- 矩阵方积
Abstract: Almost all of the existing results on the explicit solutions of the matrix equation AX-XB=C are obtained under the condition that A and B have no eigenvalues incommon For both symmetric or skewsymmetric matrices A and B.we shall give outthe explicit general solutions of this equation by using the notions of eigenprojections The results we obtained are applicable not only to any cases of eigenvalues regardlessof their multiplicities but also to the discussion of the general case of this equation.
- matrix cquation /
- explicit solution /
- eigenprojection matrix squareproduct /

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参考文献(15)

[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=A^TX 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 Σ_r-1^mU^m-r×U^r-1=C.Comput.Methods Appl.Mech.Engrg.115(1994).359-364.