This question is particularly in the context of the word embedding algorithm Word2Vec.
I've noticed that many examples that are given in the original paper and other blog posts say things like
vec(king) - vec(man) + vec(woman) = vec(queen) or
vec(Madrid) - vec(Spain) + vec(France), but how is it determined when to use addition and when to use subtraction?
Intuitively, one can deduce that subtracting the country name from the capital and adding another country name would provide information on the new country's capital, but I was wondering if there was a formal explanation on how exactly this process goes.