矩阵行最简式的唯一性

UNIQUENESS OF THE SIMPLEST FORM OF A MATRIX FOR ROWS

分析了具有等价行向量组的两矩阵之间行向量组、列向量组及矩阵所对应的齐线性方程组的解之间关系，通过对行最简式定义的分析，得出两个结论：１．行最简式相同是矩阵行向量组等价的充要条件，２．矩阵行最简式是唯一的。使得对向量组等价性的研究转化为只需对矩阵作行初等变换即可实现，得到了研究向量组等价性的一种简洁、有效的方法，同时使得行最简式在矩阵研究中变得更为重要。

Analyzes the row rectors and column vectors of two matrices with equivalentrow vectors and the solutions of the homogeneous linear equations associated with thosematrices. Two conclusions follow from the definition of the row simplest form: 1. The equality of row simplest forms is the necessary and sufficient condition of the equivalence ofrow vectors of matrices. 2. The simplest form of a matrix is unique. The study of equivalence of vectors be reduced to the row elementary transformations of a matrix, and thissimple, effective method makes the row simplest form more important.