前面在写南开大学2019年研究生入学考试高等代数第7题时提到了Roth定理,有网友在知乎评论提到了J. K. BaksalaryandR. Kala在1978年发表了一个简洁的证明,我刚刚下载看完了,确实比Roth原先给的证明简洁了很多,论文写得很精彩,于是特地分享给大家。 参考文献 [1]H. Flanders, On the matrix equation AX-XB=C an...
O. Vorontsov, "The matrix equation X + AX TB = C: Conditions for unique solvability and a numerical algorithm for its solution," Dokl. Math. 85, 265-267 (2012). 2. Yu. O. Vorontsov and Kh. D. Ikramov, "Numerical solution of matrix equations of the form X +...
-X~+Yz=O. SolutionoftheMatrixEquationAX-XB=C 353 Respectively,multiplying the 1st, 2nd ... ,/-th terms of (11) by I, B,..., B z § 1, and then adding up, we have A(Xo+X 1B+ ... + XzB ~)-(Xo+X1 B+ ... +XzB~)B=-C i.e., X= -(Xo + XI B+ ... + X,...
The matrix equation AX + XB = C , where XB is obtained by the entry-wise conjugation of X , is examined. On the basis of analogy with the Sylvester matrix... Ikramov,D Kh. - 《Computational Mathematics & Mathematical Physics》 被引量: 0发表: 2016年 The criteria of the matrix equatio...
Matrix equation AXB = Creproductive equationreproductive solutionIn this paper we represent a new form of condition for the consistency of the matrix equation AXB = C . If the matrix equation AXB = C is consistent, we determine a form of general solution which contains both reproductive and ...
The well-known Roth's equivalence theorem states that the matrix AX+YB=C is solvable for X and Y if and only if AC0B and A00B are equivalent, i.e. ran... Y Tian - 《J.concr.appl.math》 被引量: 0发表: 2004年 Solution of the Sylvester matrix equation AXB + CXD = E A ...
A necessary and sufficient condition for the matrix equation AXB+ CYD= E to be consistent is established, and if it is, a representation of the general solution is given, thus generalizing earlier results concerning the equation AX+ YB= C....
Karger, S. Yekhanin, The complexity of matrix completion, in: Proceedings of the Seventeenth Annual... There are more references available in the full text version of this article. Cited by (12) The solution of the matrix equation AXB=D and the system of matrix equations AX=C,XB=D with...
The paper investigates a rational approximation problem in connection with the convergence analysis of the ADI iterative method applied to the matrix equation X AXB= C. In the real case, a complete theory on the characterization and unicity of the optimal solution as well as on the convergence ...
一、Matrix equation(一)例子 二、矩阵等式、向量等式、方程系统(增广矩阵)同质 三、解存在(一)解存在理论 四、计算(一)计算 (二)计算性质