矩阵初等变换的若干应用
Some applications of elementary
transformation of matrix
专 业: 数学与应用数学
作 者:
指导老师:
学校 二○一
摘 要
本文介绍了矩阵初等变换在高等代数中的一些应用, 总结了其在求矩阵和向量组的秩、求逆矩阵、化二次型为标准形、求解矩阵方程以及求一元多项式最大公因式中的应用.
关键字: 初等变换; 秩; 逆矩阵; 标准形; 矩阵方程; 最大公因式
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Abstract
In this paper, we introduce some applications of elementary transformation of matrix in algebra, and summarizes the applications of elementary transformation of matrix in the rank of a matrix and vector, the inverse matrix, changing quadratic form as the standard form,
solving the matrix equation and the monadic polynomial greatest common factor.
Keywords: elementary transformation; rank; inverse matrix; standard form; matrix
equation; greatest common factor
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