Theorem 1. two matrices and are sim

定理1的两个矩阵和是相似的，当且仅当它们的特性矩阵是等价的：<br>。<br>这个定理是非常重要的。它不仅给出了两个矩阵是相似的充分必要条件，但是，更重要的是，它改变了相似关系到一个等价关系。<br>这是我们难以对付的相似性关系，但是，使用基本的操作，我们可以做出等价关系更加具体。然而，我们只给出定理，没有它的证明的结论。这里的特性矩阵是-matrices。然而，-matrices的等价概念还没有被赋予任何。因此上述定理的证明之前，我们首先要确定一些概念，如基本操作对-matrices概念，二-matrices等价的概念。

Theorem 1. two matrices and are similar if and only if their characteristic matrices are equivalent:<br>.<br>This theorem is very important. It not only gives the necessary and sufficient condition for two matrices to be similar, but, more importantly, it changes the similarity relation into an equivalence relation.<br>It is difficult for us to deal with a similarity relation, but, using elementary operations, we can make the equivalence relation more specific. However we have given only the conclusion of the theorem, no its proof. Here the characteristic matrices are -matrices. However, the equivalence concept of -matrices has not been given either. Therefore before a proof of the above theorem we first have to define some concepts, such as the concepts of elementary operations on -matrices, the concept of equivalence of two -matrices.

定理1。两个矩阵，且仅当其特征矩阵等价时相似：<br>.<br>这个定理很重要。它不仅给出了两个矩阵相似的充要条件，而且更重要的是将相似关系转化为等价关系。<br>处理一个相似关系是困难的，但通过初等运算，可以使等价关系更加具体。然而，我们只给出了定理的结论，没有给出它的证明。这里的特征矩阵是-矩阵。然而，-矩阵的等价概念也没有给出。因此在证明上述定理之前，我们首先要定义一些概念，如矩阵的初等运算的概念，两个矩阵等价的概念。<br>