惯性定律的新证法

The New Method for Proving the Law of Inertia

本文从实对称矩阵的角度 ,给出了惯性定律的一种新证法 .这种证法可使我们从已给的一个实二次型 f( x1 ,x2 ,… ,xn) =∑ni,j=1aijxixj 的矩阵 A=( aij) n× n的诸元素 ,来直接研究这个二次型的性质的这一体系更加完整 .同时 ,本文还大大地改进了雅可比方法 ,使雅可比的方法更加完美 ,应用更加广泛 .

From the point of view about the real number symmetrical matrix, the article gives us a new method for proving the law of inertia. From some elements of the matrix A=(a ij ) n×n , which comes from a given real number quadrics f(x 1,x 2,…,x n)=∑ni,j=1a ij x ix j, this method gives us a way to study directly the quadrics' property and make this way pass unimpeded . At the same time, this article also improves greatly “Jacobi's method” and make it more perfect and wider in application .