E^n中的一个三角不等式

A TRIANGLE INEQUALITY IN E￣n

本文直立了Ｅｎ中的Ｎ（Ｎ＞ｎ≥２）个定向超平面两两之间夹角的正弦不等式．

Theorem: Let P1,P2, ..',PN (N > n ≥ 2 ) be directed hyperplanes of which at least two aren′t parallel, if the angle formed by Pi, Pi is PiPj=Oij and mi is positive number (i,The necessary and sufficient conditions of the equality holding is that the rank of matrix A= (mimjsin2)n×n is n + 1 and the negative characteristic roots of A are equal.