齐线性方程组AX=0的反问题研究

THE REVERSION QUESTION'S RESEARCH OF THE HOMOGENEOUS LINEAR EQUATION AX=0

本文研究n个未知量的齐线性代数方程组的反问题在实对称矩阵类中解的结构,主要结果是:反问题在实对称矩阵类中解的全体构成R^(n×n)的n(n-1)/2维线性子空间。

In this paper, we researched the reversion solution's structure of the equation AX = 0, where X be given a nonzero vector, and A belong to the nth real symmetry matrices. LetK(X)= {A\A ∈ Ra×a,AT = A and AX = 0} (1)then, the main result is that K(X) will be the n(n-1)/2 dimensional linear subspace in the matrices space Ra×a.