线性双空间张量方程φijAiXBj＝C

陈玉明; 肖衡; 李建波

线性双空间张量方程φ_ijAⁱXB^j＝C

1.
湖南大学应用数学系, 长沙 410082;
2.
北京大学数学系, 北京 100871;
3.
美国肯塔基大学数学系, 勒星顿 KY 40506-0027

计量
- 文章访问数: 2263
- HTML全文浏览量: 75
- PDF下载量: 455
- 被引次数: 0
出版历程
- 收稿日期: 1996-02-16
- 刊出日期: 1996-10-15

The Linear Bi-Spatial Tensor Equation φ_ijAⁱXB^j=C

Chen Yuming¹,
Xiao Heng²,

1.
Department of Applied Mathematics, Hu'nan University, Hu'nan 410012, P.R. China;
2.
Department of Mathematics, Peking University, Beijing 100871, P. R. China

摘要

摘要: 本文在对系数张量的特征值不作任何限制的条件下,得到了一类线性双空间张量方程的显式解。这类方程包含了许多经常遇到的方程作为其特例。
- 张量方程 /
- 双空间张量 /
- 方张量积
Abstract: A linear bi-spatial tensor equation which contains many of ten encotuntered equations as particular cases is thoroughly studied Explicit solutions are obtained. No conditions on eigenvalues of coefficient tensors are imposed.
- tensor equation /
- hi-spatial tensor /
- square tensor-product

HTML全文

参考文献(29)

[1]	M, Wedderburn,Note on the linear matriz equation, Proc, Edirtgburgh Math,Soc.,22 (1904),49-53.
[2]	D,Z,Rutherford, On the solution of the matriz equation AX+XB=C,Nederl,Wetensch, Proc.,Ser,A,35(1932),53-59.
[3]	W,E, Roth,The equation AX-YB=C and AX-XB=C in matrices, Proc,Amer,Math, Soc.,3(1952),392-396.
[4]	M,Rosenblum,On the operator equation BX-XA=Q,Duke Math,J.23 (1956),263-270
[5]	G, Lumer and M, Rosenblum, Linear operator equations, Proc,Amer, Math,Soc.,10 (1959),32-41.
[6]	Ma Er-chieh, A finite series solution of the matrix equation AX-XB=C,SIAM J,Appl,Math.,14 (1966),490-495.
[7]	R.A,Smith,Matrix equation XA+BX=C,SIAM J.Appl,Math.,16(1968),198-201.
[8]	A.Jameson, Solution of the equation AX+XB=C by inversion of a MXM or NXN matrix SIAM J, Appl, Math.,16(1968),1020-1023.
[9]	M, Rosenblum, The operator equation BX-XA=Q with selfadjoint A andB,Proc,Amer,Math,Soc.,20 (1969),115-120.
[10]	P, Lancaster, Explicit solutions of linear matrix equations, SIAM Reviews,12 (1970),544-566.
[11]	P,C, Müiller,Solution of the matrix equation AX+XB=-Q and S^TX+XS=-Q,SIAM J,Appl,Math.,18 (1970),682-687.
[12]	R.E, Hartwig, Resultants and the solution of AX-XB=C,SIAM J,AppI,Math.,23 (1972),104-117.
[13]	R.H, Bartels and G,W.Stewart,Solution of the equation AX+XB=C,Comm,ACM,15(1972),820-826.
[14]	V,Kucěra,The matrix equation AX+XB=C,SIAM J.Appl, Math.,26(1974),15-25.
[15]	W.T.Vetter,Vector structures and solutions of linear m atria equations,Linear Algebra Appl.,10(1975),181-1889.
[16]	.
[17]	J.Z,Hearson,Nonsingular solutions of TA-BT=C.Linear Algebra Appl.,16 (1977),57-83.
[18]	A, Bickart, Direct solution method for A_{1<.sub>E+EA₂=-D, IEEE Trans, Auto.Control, 22(1977),467-471.}
[19]	H,Flanders and H.K, Wimmei, On the matrix equations AX-XB=C and AX-YB=C,SIAM J,Appl,Math.,32(1977),707-710.
[20]	G.H, Golub,S Nash and C.Van Loan, A Hessenberg-Schur method for the matrix problem AX+XB=C,IEEE Trans.Auto.Control AC 24 (1979),909-913.
[21]	S,P, Bhattacharyya and E, Desouta, Controllability,observability and the solution of AX-XB=C,Linear Algebra Appl.,39 (1981),16 7-188.
[22]	J,R.Magnus, L-structured matrices and linear matrix equations,Linear and Mulfilinear Algebra, 14 (1983),67-88
[23]	B,N, Datta and K, Datta, The matrix equation XA=A^TX and an associated algorithm for solving the inertia and stability problems,Linear Algebra Appl.,87(1987),103-119.
[24]	J.H Bevis. F,J. Hall and R.E, Hariwig, The matrix equation Ax-XB=C and its special cases,SIAM J.Matrix Anal,Appl,9(1988),348-359.
[25]	K,Datta,Thematrix equation XA-BX=R and its applications,Linear Algebra Appl.109(1988),91-105.
[26]	高维新,矩阵方程AX-XB=C的连分式解法,中国科学,A辑,(6) (1988),576-584.
[27]	F, Rotella and P, Borne, Explicit solution of Sylvester and Lyapunov equations, Math, Comput, Simulation, 31(1989),27-1281.
[28]	P.S,Szczepaniak, A contribution to matrix equations arising in system theory, Math,Meth.Appl,Sci.,15 (1992),593-597.
[29]	Guo Zhongheng, Th, Lehmann, Liang Haoyun and C,-S,Man,Twirl tensors and the tensor equation AX-XA=C,T.Elasticity,27 227-245.(1992).