摘要
为了更容易对二次曲面进行分类,结合微积分中比较常用的稳定点和线性代数中非常重要的矩阵特征值的概念,在不同情况下给出了二次曲面的简化方程的直观特点,并根据二次曲面所对应的二次函数是否有稳定点以及它的二次项部分矩阵的非零特征值的个数与符号给出了判别一个一般二次曲面类型的充要条件。
In order to get the classification of general quadric surfaces more easily,by combining the concept of stable point commonly used in calculus and matrix eigenvalue in linear algebra,simplified equations of general quadric surfaces for different cases were characterized.Then,sufficient and necessary conditions for quadric surfaces classification based on the stable points of their corresponding quadratic functions and the number and the sign of non-zero eigenvalues of the matrix of their quadratic terms were given.
出处
《中国科技论文》
CAS
北大核心
2015年第5期602-607,共6页
China Sciencepaper
基金
北京服装学院教改资助项目(ZDJG-1310)
北京航空航天大学教改资助项目
关键词
二次曲面
简化方程
分类
稳定点
特征值
quadric surface
simplified equations
classification
stable point
eigenvalue of a matrix
