关于n维欧氏空间E^n中的两个任意维平面的单维夹角与多维夹角

ON THE 1-DIMENSIONAL ANGLES AND MULTIDIMENSIONAL ANGLES BETWEEN TWO MULTIDIMENSIONAL PLANES IN E^N

本文首先讨论了n维欧氏空间E^n中两个任意维数平面相互之间的单维夹角组之间的关系;然后给出了两个任意维数平面之间的单维角组与多维角的一个有关等式;最后指出E^n中任意维数平面的夹角公式是直观空间中直线及平面之间夹角公式的自然推广。

This paper first dealed with the relationship between the set of 1-dimensional aggies of S_1 with S_2 and the set of 1-dimensional angles of S-2 with S_1, where S_1 and S_2 are h-dimensinal plane and k-dimensional plane in E^n respectively. Then the equality was introduced and proved, where θ is the multidimensional angle of S_1 with S_2 and θ_(11),θ_(12), …,θ_(1h) are the 1-dimensional angles of S-1 with S_2.