矩阵空间的二次矩阵基与基秩

The Quadratic Matrix Basis and Base Ranks of Matrix Space

当n≥2时,证明了矩阵空间C^n×n存在着由二次矩阵构成的基(即二次矩阵基),给出了二次矩阵基的基秩及其等价分类的相关不等式,指出当n=2,3时,Cn×n的二次矩阵基秩的等价分类的不等式实质为等式.

This paper proves that when n≥2,there exists the basis of matrix space c^n×n composed of quadratic matrices.It shows some inequalities of base ranks of quadratic matrix basis and their equivalence class,and points out that the inequality for the equivalence class of the base ranks of quadratic matrices is an equation actually,when n=2,3.