实对称矩阵特征值的一种在几何学上的应用  

Application of Real Symmetric Matrix Eigenvalues in Geometry

作　　者：孙卫卫[1] 

机构地区：[1]青岛理工大学琴岛学院,山东青岛266106

出　　处：《佳木斯大学学报（自然科学版）》2015年第4期634-635,640,共3页Journal of Jiamusi University：Natural Science Edition

摘　　要：实际问题中,经常遇到一些形式较为复杂的二次曲线与二次曲面.对它们形状的研究也是必要的.本文主要从实对称矩阵特征值的角度对于形如a11x2+a22y2+2a12xy+c1=0的二次曲线与形如b11x2+b22y2+b33z2+2b12xy+2b13xz+2b23yz+c2=0的二次曲面的形状进行推断.从而体现了实对称矩阵特征值的一种在几何学上的应用.Some quadratic curves and quadratic surfaces of the more complex form are often given in the practical problems. It is necessary to study their shapes. In this paper,mainly from the angle of real symmetric matrix eigenvalue,the shapes of quadratic curves and quadratic surfaces were deduced. Thus,the application of real symmetric matrix eigenvalue in geometry was embodied.

关 键 词：实对称矩阵 特征值 二次曲线 二次曲面 正交矩阵 正交变换. 

分 类 号：O13[理学—数学]