一种避免除法运算的矩阵的秩的计算方法

Calculating Rank of Matrix without Using Division Operation

在高等代数中,通常采用初等行变换计算矩阵的秩和行空间的基。该方法不可避免地涉及到除法运算,使得计算中出现很多分数,从而导致出错率和运算量增加。针对上述情况,给出一种新的矩阵秩的求解方法,该方法可以有效的避免除法运算,从而实现了对初等行变换的改进。

In most of advanced algebra textbooks,to determine the rank of a matrix and a basis for its row space,students are usually instructed to reduce this matrix to equivalent echelon form by using elementary row operations.This approach encounters division inevitably,thus a lot of fractional numbers are appeared during the calculation.Therefore,this method can eliminate errors in operation and improve the transformation of elementary row.