数学毕业论文矩阵分解与矩阵方程AX=BAXB=C的解.doc

数学毕业论文-矩阵分解与矩阵方程AX=B，AXB=C的解  矩阵分解和矩阵方程AX=B，AXB=C的解摘要本文详细地阐述了矩阵的QR分解，奇异值分解，利用这些矩阵分解，给出了矩阵方程AX=B， AXB=C有解条件及有解时解的1般表达式。关键词：初等变换；QR分解；奇异值分解；矩阵方程。Matrix Decomposition and the Solutions of the Matrix Equations AX=B,AXB=CAbstractIn this paper,  the QR decomposition,  Singular Value decomposition of matrix have been remarked in detail.Using these matrix decompositions,  the necessary and sufficient conditions of the matrix equations  AX=B  andAXB=C  have a solution and have an unique solution are given.  And when the matrix equations have a Solution or  have an unique solution, the expression of the solution has been presented. Key Words:  Fundamental transformation; QR decomposition; Singular value decomposition; matrix equation.目   录1引言……………………………………………………………………………………………12矩阵的两种分解………………………………………………………………………………1  2.1  QR分解…………………………………………………………………………………22.2  奇异值分解………………………………………………………………………………23 AX=B的解法 …………………………………………………………………………………4  3.1矩阵 可逆……………………………………………………………………………6  3.2  矩阵 为满秩矩阵……………………………………………………………………7  3.3   不可逆………………………………………………………………………………7  3.4典型题举例……………………………………………………………………………74 AXB=C的解法 ………………………………………………………………………………12 4.1  若 ， 均可逆…………………………………………………………………………14  4.2  若 （ ）可逆， （ ）不可逆………………………………………………………14  4.3  若 ， 均不可逆………………………………………………………………………14  4.4  典型题举例……………………………………………………………………………145结束语…………………………………………………………………………………………186参考文献………………………………………………………………………………………19【包括：毕业论文、开题报告、任务书】【说明：论文中有些数学符号是编辑器编辑而成，网页上无法显示或者显示格式错误，给您带来不便请谅解。】