n×n对称矩阵空间的对称基及其基秩不等式

Symmetric Basis of n×n Symmetric Matrix Space and Its Base Rank Inequality

在给出数域P上的n×n阶对称矩阵空间S n×n(P)的最小基秩的对称基的基础上,证明了S n×n(P)的对称基的基秩不等式的最大下界和最小上界是可达的,得到了每个对称矩阵在最小基秩、最大基秩的对称基下的线性组合的显示表达式.

The symmetric basis of the minimum basis rank of n×n symmetric matrix space S n×n(P)over number field P is given firstly,then the maximum lower bound and the minimum upper bound of the base rank inequality of symmetric basis of S n×n(P)are proved to be reachable.And the explicit expression of linear combination of symmetric matrices under symmetric basis with the minimum and the maximum basis rank are obtained respectively.