实数域上对称矩阵空间的保秩函数

Functions preserving rank of symmetric matrices over real fields

令S_n(R)表示R上所有n×n对称矩阵所组成的空间,设f是R→R的一个函数,若f满足rankA=ranf(A),(?)A∈S_n(R),称f为S_n(R)上的保秩函数,刻画了n≤3时S_n(R)上保秩函数的形式。

LetSn（R）be the space of all n×n symmetric matrices over real fields. For a function f：Sn（R）→4 Sn （R） , if rankA = ranf（A）, VA ∈ Sn （R）, then f is called a function preserving rank of symmetric matrices. In this paper, we characterize the functions of preserving rank on symmetric matrices when n ≤ 3.