Coordinate functional
= Coordinate functional
{title2=$e_i^*(\sum_j a_je_j)=a_i$}
A <coordinate functional> extracts one coefficient in a specified finite <basis>. It is an element of that <basis>'s <dual basis>, rather than a coordinate rule independent of the <basis>. For the <standard basis> of $F^n$, the $i$th <coordinate functional> sends $(a_1,\ldots,a_n)$ to $a_i$.