矩阵分解和矩阵方程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=C

Abstract

In 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 and

AXB=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.