数学毕业论文-矩阵分解与矩阵方程AX=B，AXB=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……………………………&hell