如何标准化零向量 [英] How do you normalize a zero vector

问题描述

假设您有一个规范化"函数，该函数将一个数字列表(代表一个矢量)作为输入并返回规范化的矢量.向量全为零或向量的总和为零时，结果应该是什么?

Suppose you have a function 'normalize' which takes a list of numbers (representing a vector) as input and returns the normalized vector. What should the result be when the vector is all zeros or the sum of its components is zero?

推荐答案

从数学上讲，零向量无法归一化.其长度将始终为0.

Mathematically speaking, the zero vector cannot be normalized. Its length will always remain 0.

对于给定的向量v = (v1, v2, ..., vn)，我们有:||v|| = sqrt(v1^2 + v2^2 + ... + vn^2).让我们记住，归一化向量是具有||v||=1的向量.

For given vector v = (v1, v2, ..., vn) we have: ||v|| = sqrt(v1^2 + v2^2 + ... + vn^2). Let us remember that a normalized vector is one that has ||v||=1.

因此对于v = 0，我们有:||0|| = sqrt(0^2 + 0^2 + ... + 0^2) = 0.您永远无法将其标准化.

So for v = 0 we have: ||0|| = sqrt(0^2 + 0^2 + ... + 0^2) = 0. You can never normalize that.

同样重要的是要注意确保一致性，您不应返回NaN或任何其他空值. v=0的规范化形式确实是v=0.

Also important to note that to ensure consistency, you should not return NaN or any other null value. The normalized form of v=0 is indeed v=0.

这篇关于如何标准化零向量的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！