x*****o
发帖数: 28 | 1 多维空间角怎么定义？
两个n维向量(x1,x2,...,xn) (y1,y2,...,yn)之间夹角?
n维向量与一个超平面间夹角? (是否 90degree - 夹角(超平面法向量,n维向量)?)
高维空间与2/3-维有什么区别? Thanks!
在google上搜什么关键词,可以搜到相关信息?
high dimension angle? 搜到好多,稍微看了下,似乎很多没用..
谢谢！:)... | y***u
发帖数: 101 | 2 For two vectors, simply look at the plane spanned by them
and measure the angle on the plane.
For two d-dim subspaces in a n-dim space, look at their intersection I,
which is a (d-1)-dim subspace. Let K be an (n-d+1)-subspace perpendicular
to I. Draw a (n-d)-sphere in K, centered at the projection of I on K,
and look at the fraction of the sphere bounded by the two subspaces.
If the two subspaces have different dimensions, project one onto another.
【在 x*****o 的大作中提到】
: 多维空间角怎么定义？
: 两个n维向量(x1,x2,...,xn) (y1,y2,...,yn)之间夹角?
: n维向量与一个超平面间夹角? (是否 90degree - 夹角(超平面法向量,n维向量)?)
: 高维空间与2/3-维有什么区别? Thanks!
: 在google上搜什么关键词,可以搜到相关信息?
: high dimension angle? 搜到好多,稍微看了下,似乎很多没用..
: 谢谢！:)...
| x*****o
发帖数: 28 | 3 oo. thanks.
dot product can be extended into n-dim. Angles between n-d vectors can be
solved.
N vector A
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