THE EXPLICIT SOLUTION OF THE MATRIX EQUATION AX-XB=C——To the memory of Prof. Guo Zhongheng

Applied Mathematics and Mechanics (English Edition) ›› 1995, Vol. 16 ›› Issue (12): 1133-1141.

THE EXPLICIT SOLUTION OF THE MATRIX EQUATION AX-XB=C——To the memory of Prof. Guo Zhongheng

陈玉明¹, 肖衡²

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

收稿日期:1995-02-28 出版日期:1995-12-18 发布日期:1995-12-18
通讯作者: Chien Weizang
基金资助:
Project Supported by the National Natural Science Foundation of China

THE EXPLICIT SOLUTION OF THE MATRIX EQUATION AX-XB=C——To the memory of Prof. Guo Zhongheng

Chen Yuming¹, Xiao Heng²

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

Received:1995-02-28 Online:1995-12-18 Published:1995-12-18
Supported by:
Project Supported by the National Natural Science Foundation of China

摘要/Abstract

摘要： 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 eigenprojectionsThe 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.

陈玉明;肖衡. THE EXPLICIT SOLUTION OF THE MATRIX EQUATION AX-XB=C——To the memory of Prof. Guo Zhongheng[J]. Applied Mathematics and Mechanics (English Edition), 1995, 16(12): 1133-1141.

Chen Yuming;Xiao Heng. THE EXPLICIT SOLUTION OF THE MATRIX EQUATION AX-XB=C——To the memory of Prof. Guo Zhongheng[J]. Applied Mathematics and Mechanics (English Edition), 1995, 16(12): 1133-1141.

参考文献

[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譓 or N譔 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] Gao Weixing, Continued-fraction solution of matrix equation AX-XB=C.Scientia Sinica Ser.A.,32(1989).1025-1035.
[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 Σ_r-1^mU^{m-r譛^r-1=C.Comput.Methods Appl.Mech.Engrg.115(1994).359-364.}

THE EXPLICIT SOLUTION OF THE MATRIX EQUATION AX-XB=C——To the memory of Prof. Guo Zhongheng

THE EXPLICIT SOLUTION OF THE MATRIX EQUATION AX-XB=C——To the memory of Prof. Guo Zhongheng

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 0

编辑推荐

Metrics

本文评价