language agnostic - How do you normalize a zero vector

Question

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?

Answer 1

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

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.

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

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.