Solutions of the Matrix Equation AXB + CXD = E

机译：矩阵方程aXB + CXD = E的解

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Solutions of the general linear matrix equation summation A sub i XB sub i = c where i = 1 and N is the limit are obtained and presented in this thesis. Some special cases do arise like the Lyapunov matrix equation. Necessary conditions and sufficient conditions are established for the solution of the general linear matrix equation. Other forms of solutions than those obtained through the use of similarity transformations that have been considered make use of the spectral decomposition of matrices and tensor products of matrices or Kronecker products. In considering the general linear matrix equation, linear matrix equations in which two different variables appear are also studied. Conditions for the existence of a solution for this type of equation are given. The theory of the generalized inverses of a matrix was used in obtaining a solution to the general linear matrix equation. More general forms of the solution are given and conditions under which these solutions exist have been established. Solutions to systems of matrix equations were also considered. As a by-product of this investigation, some aspects of the model reduction problem may be treated from the point of view of matrix equations.

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作者
Pomykalski, T. S.;
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年度 1979
页码 p.1-106
总页数 106
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Matrices(Mathematics); Solutions(General); LInear algebraic equations; Covariance; Theses;

机译：矩阵（数学）;解（通用）; LInear代数方程;协方差;论文;

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1. Least-Squares Solutions of the Matrix Equations AXB + CYD = Hand AXB + CXD = H for Symmetric Arrowhead Matrices and Associated Approximation Problems [J] . Yongxin Yuan Journal of applied mathematics . 2014,第Pta6期

机译：矩阵方程的最小二乘解AXB + CYD =手AXB + CXD = H对于对称箭头矩阵和相关近似问题
2. An iterative algorithm for the generalized reflexive solution of the matrix equations AXB = E, CXD = F [J] . Chen D., Yin F., Huang G.-X. Journal of applied mathematics . 2012,第Pta8期

机译：矩阵方程AXB = E，CXD = F的广义自反解的迭代算法
3. LSQR iterative common symmetric solutions to matrix equations AXB = e and CXD = F [J] . Chen Y., Peng Z., Zhou T. Applied mathematics and computation . 2010,第1期

机译：矩阵方程AXB = e和CXD = F的LSQR迭代公共对称解
4. Circulant Solutions of the Matrix Equations AX=C and AXB=C [C] . Aldous Cesar F. Bueno International Conference on Mathematical Sciences . 2014

机译：矩阵方程的循环解决方案AX = C和AXB = C.
5. Low-rank solution methods for large-scale linear matrix equations. [D] . Shank, Stephen D. 2014

机译：大规模线性矩阵方程的低秩求解方法。
6. An Iterative Algorithm for the Reflexive Solution of the General Coupled Matrix Equations [O] . Zhongli Zhou, Guangxin Huang 2013

机译：一般耦合矩阵方程自反解的迭代算法
7. The solution of the matrix equations AXB−CXD=E AND (YA−DZ,YC−BZ)=(E,F) [O] . Chu King-wah Eric 1987

机译：矩阵方程AXB-CXD = E AND（YA-DZ，YC-BZ）=（E，F）的解

Solutions of the Matrix Equation AXB + CXD = E

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