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本文利用四元数矩阵方程AX-XB=C有唯一解的充要条件给出了两个定理,并讨论了特殊条件下四元矩阵方程AX-XB=C在C=0和C=0且A=B两种情况下解的性质. 相似文献
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讨论矩阵方程sum from k=0 to r( )A~kXB~k=F存在惟一解的充要条件,并给出了两种迭代求解法. 相似文献
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Fanliang Li Xiyan Hu Lei Zhang 《高等学校计算数学学报(英文版)》2006,15(3):217-226
In this paper, least-squaxes mirrorsymmetric solution for matrix equations (AX = B, XC = D) and its optimal approximation is considered. With special expression of mirrorsymmetric matrices, a general representation of solution for the least-squares problem is obtained. In addition, the optimal approximate solution and some algorithms to obtain the optimal approximation are provided. 相似文献
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Qiu Yuyang Qiu Chunhan 《高校应用数学学报(英文版)》2007,22(4):441-448
The matrix equation AXB = E with the constraint PX=sXP is considered,where P is a given Hermitian matrix satisfying p~2=I and s=±1.By an eigenvalue decomposition of P,the constrained problem can be equivalently transformed to a well-known unconstrained problem of matrix equation whose coefficient matrices contain the corresponding eigenvector, and hence the constrained problem can be solved in terms of the eigenvectors of P.A simple and eigenvector-free formula of the general solutions to the constrained problem by generalized inverses of the coefficient matrices A and B is presented.Moreover,a similar problem of the matrix equation with generalized constraint is discussed. 相似文献
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胡端平 《应用数学与计算数学学报》1998,12(1):77-82
本文推广了R.Penrose关于矩阵方程组AX=C,XB=D的工作,给出了矩阵方程组 A_1XB_1=C_1,A_2XB_2=C_2的相容性条件,给出了通解表达式以及唯一解的充要条件。 相似文献
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讨论了矩阵方程AXAT+BYBT=C关于亚半正定矩阵X,Y有解的充要条件,并在有解时给出了解的通式. 相似文献
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矩阵方程AX-X~TB=C的解 总被引:1,自引:0,他引:1
通过引入矩阵的广义逆构造性地给出矩阵方程 AX-XTB=C的特解 ,同时通过不同的方法给出其所对应的齐次方程 AX-XTB=O解的两种不同形式 .从而得到了矩阵方程 AX-XTB=C两种不同形式的解 . 相似文献