论二次型的定义

A DISCUSS ABOUT THE DEFINITION OF QUADRATIC FORM

由于对K次齐次多项式理解的不同。从而引起对二次型概念理解上的差异。因此提出一个统一的K次齐次多项式的定义为:其中而二次齐次多项式是上述定义中K=2的特殊情形。这样二次型就包含了零多项式,从而解决了把零多项式排除在二次型外带来的二次型理论中的某些矛盾现象。

A unified definition of homogeneous polynomials of degree K is given as f(x1 ,x2,… ,xn) = Σk1, ,k2, … ,kn α,[k1,k2,…kn]x1[k1]x2[k2]…xn[kn]where a[k1,k2…,kn]∈P, Σ n/i=1 ki=k. Such that the homogeneous polynomials of degree 2 become the particular case of above definition provided K=2. As a result, the quadratic form will contain zero - polynomial so that some contradictions in theory on quadratic form caused by excluding zero-polynomial from quadratic form is eliminated.