摘要
本文研究了ｎ维射影空间中的逆射变换的确定、性质及其一类特殊变换——配极变换的性质．从射影几何角度证明了如下结论：在Ｐｎ中对非退化的二次曲面Σ：∑ｎ＋１ｉ，ｊ＝１ａｉｊｘｉｘｊ＝０，ａｉｊ＝ａｊｉ，｜ａｉｊ｜≠０．经过适当的射影变换，即选择恰当的自共轭ｎ＋１面体作为参考坐标ｎ＋１面体时便可把二次曲面方程化简为标准式：ｂ１ｘ２１＋ｂ２ｘ２２＋…
,In this paper, the criterion and properties of inverse projective transformation and a special transformation involutory projective transformation in n dimensional projective spaces is studied. At a projective geometry angle,it is proved that for a non degenerate quadric surfaceΣ:∑n+1i,j=1aijxixj=0,aij=aji,|aij|≠0 by selecting a correct self conjugate n+1 planes body as coordinate n+1 planes body,the brief form of quadric surface is ,,,b1x21+b2x22+…+bn+1x2n+1=0 .
出处
《郑州大学学报（自然科学版）》
1997年第4期26-30,共5页
Journal of Zhengzhou University (Natural Science)
关键词
射影变换
射影空间
逆射
配极
,n dimensional projective transformation
n dimensional involutory projective transformation
self conjugate n planes body
