楼上好象是用软件翻译的吧本文在第一部分首先介绍了线性空间、线性变换、根子空间、半单线性变换和幂零线性变换的概念,This article introduced concepts of linear spaces, linear transformations, semi-simple linear transformations, nilpotent linear transformations and root subspaces in the first part. 然后对这些概念的一些基本性质进行了证明.The some basic properties of the concepts are proved. 在第二部分给出了本论文的主要结论.In the second part, we give the main conclusions of the paper. 利用关于根子空间、半单变换和幂零变换的一些性质,结合了矩阵的特征根与特征向量的基本运算,Using properties of the semi-simple linear transformations, nilpotent linear transformations and the root subspaces and associating the eigenvalues and the eigenvectors of the matrix ,证明了:we prove: 1. 线性空间的任意一个线性变换可唯一的分解为一个半单变换和幂零变换的乘积,且二者具有可交换性; 1. Any linear transformation of the linear space can be uniquely decomposed into a sum of the semi-simple linear transformation and the nilpotent transformation;2.线性变换的不同特征根的特征向量的线性无关性; 2. The eigenvectors of different engienvalues are orthogonal; 3. 线性变换的特征子空间的维数与它的特征根重数的关系.3. The relations between the dimensions of characteristic subspaces of linear transformations and the multiplicities of engienvalues.