星座图欧氏距离计算
公式: d 2 ( a , b ) = | a | 2 + | b | 2 - 2Re( ab * ); (1) 证明: 令 c = a - b; 则 | c | 2 = d 2 ( a , b ) = | a | 2 + | b | 2 -2| a || b |cos< a , b >(余弦定理); (2) 令 a = | a |e jθ a b = | b |e jθ b 则 ab * = | a || b |e j(θ a -θ b ) = | a || b |cos(θ a -θ b ) + j| a || b |sin(θ a -θ b ) (欧拉公式) 于是Re( ab * ) = | a || b |cos(θ a -θ b ) = | a || b |cos< a , b > (3) 综合 (1)(2)(3) 式,得证。 来源: https://www.cnblogs.com/achangchang/p/12178283.html