一类半正定六次型及其线性性质

A Class of Positive Semi-definite Sextic Polynomial and Its Linearity Properties

应用Toeplitz矩阵、三角形两边之和大于第三边的性质与线性交换 (x ,y ,z) =(a ,b ,c)θ(0 ) ,给出了半正定三元六次型Lm(m =1,2 ,3,4 ,5 ) ,Mn,Bn(n =1,2 ,3,4 )和G1,G2 的具体表达式 ,然后给出主要结果Lm,Mn,G1,G2 ,B1,B2 及B3 +B4∈Q(A) .最后利用矩阵给出了由它们组成的线性空间的基。

Using Toeplitz matrix,the feature that the sum of the length of two sides is larger than that of the other side and the linearity transformation, the positive semi-definite sextic polynomial are derived, that is,L m(m=1,2,3,4,5),M n,B n(n=1,2,3,4) and the concrete expressions of G 1,G 2.Then the main results L m,M n,G 1,G 2,B 1,B 2 and B 3+B 4∈Q(A) are given.Finally,the cardinal number,dimensionality and linearity properties of the linear space formed by the sextic polynomial are presented.