If I have a vector $<a,b>$ is there a name or specific notation for adding the elements to create a scalar $c$, such that $c=a+b$?
For reference, I want to use this to rationalize a notion I have. With a function $f: R^{2}→R$ such that, given a vector $q=<x,y>$, $f(q)=x+y$, I want to say that the operation of summing the elements of a vector is distributive over vector addition.
I.e.
$f(<x,y>+<v,u>)=f(<x,y>)+f(<v,u>)$ because (insert name of operation here) is distributive over vector addition.