线性空间同构的应用

摘要

利用线性空间的同构，确定了数域P上的全体n元二次型作成的线性空间的维数和一组基，并证明了如果函数ex，xex，x2ex，⋯，xnex作为一组基生成线性空间L（ex，xex，x2ex，⋯，xnex），则∫xnexdx＝∑ni＝0（－1）n－in！i！xiex ＋c，c∈R。%Dimension and a base of linear space made by quadratic form with n variations are determined by isomorphisms between linear spaces.And it was proved that if the functions ex,xex,x2ex,⋯,xnex span the linear space L(ex,xex,x2ex,⋯,xnex) as a base, then ∫xnexdx=∑ni=0(-1)n-in!i!xiex +c,c∈R.