行约化梯形在子空间运算中的应用

Reduced Row Echelon Form with Applications to Subspace Operations

行约化梯形(Reduced Row Echelon Form)是线性代数中一个简单而强大的工具,在线性方程组、线性空间和数据压缩的理论和计算中有大量的应用.西方线性代数教科书普遍重视这一工具,中文教材书籍中则很少介绍,用得不多.本文详细分析和挖掘行约化梯形的性质和功能,并阐述其在线性空间的和、交、商等运算中的作用.

Reduced Row Echelon Form(RREF)is a simple but powerful tool in linear algebra,with a lot of applications to the theory and computation of linear systems,vector spaces,data compression,and so on.This tool is popular and widely used in western textbooks,but it is comparably less popular in Chinese textbooks.This note aims to give a complete exposition on RREF,and apply RREF to operations of subspace intersection,addition and quotient.