关于矩阵秩三合一定理的初等变换证明

Elementary Transformation Proof of Matrix Order Three-in-one Theorem

关于定理"矩阵的秩=矩阵的行秩=矩阵的列秩"的证明方法较多,本文将用初等变换的方法给出证明,此证明方法易于理解,便于计算机编程实现,有利于机器证明。

There are many proofs of this theorem: matrix order equals row order of matrix equals line order of matrix. This article proves it with the method of elementary transformation. This method is easy to understand, convenient to carry out the computer programming and helpful for the machine to prove.