I found a notation that $$|y_i| = y_i^{+}+y_i^{-} $$
where y is y n dimensional vector.
what does +/- imply? I understand that we can have both negative and positive value into absolute function, but eventually we will always have the positive outcomes. how can absolute value be equivalent to sum of negative value and positive value?
Best Answer
That is generally used with the meaning $y_i^+=\max(y_i, 0)$ and $y_i^-=\max(-y_i, 0)$, and the equality holds. Does it make sense for you?