同态基本定理在向量空间中的应用

Application of Homomorphic Theorem in Vector Space

本文建立了商向量空间的维数公式,在此基础上,应用同态基本定理和第一同构定理获得了对维数公式及Sylvester定理的简单、明了的证明。

This paper gives a formula of calculating the dimension of quotient space at first,based on the result,applies homomorphic theorem and isomorphic theorem I to vector space,and then gains a simple proof of dimensional formula and Sylvester theorem respectively.