Gram矩阵在不等式中的应用

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.

Applications of Gram Matrix in the Inequalities

using the positive semi-definite of the Gram matrix G x 1,x 2,…,x n,this paper first studied the applicationof the matrix G x 1,x 2,…,x n on the absolute value of the maximum inner product spaces and integral average inner product space,and then studied the Gram determinant inequalities between Γ x 1,x 2,…,x n and Γ x i.Finally,through changing the conditions of Ostrowski inequality,the author obtained some inequalities of two vectors in the inner product space.