Gram矩阵在不等式中的应用

Applications of Gram Matrix in the Inequalities

利用了Gram矩阵G(x1,x2,…,xn)的半正定性,首先研究了Gram矩阵在绝对值最大值内积空间和积分平均内积空间中的应用,然后研究了Gram行列式Γ(x1,x2,…,xn)与Γ(xi)的不等式关系.最后通过改变Ostrowski不等式的条件,得到了空间中两个向量的内积所满足的不等式.

using the positive semi-definite of the Gram matrix t;（x1 ,x2… ,xn） , tins paper first studied the applicationof the matrix G（x1 ,x2… ,xn） on the absolute value of the maximum inner product spaces and integral average inner product space, and then studied the Gram determinant inequalities between F（x1 ,x2… ,xn.） and F（xi）. Finally ,through changing the conditions of Ostrowski inequality ,the author obtained some inequalities of two vectors in the inner product space.