Definition:Coordinate System/Coordinate Function

Definition
Let $\left \langle {a_n} \right \rangle$ be a coordinate system of a unitary $R$-module $G$.

For each $\displaystyle x \in G$ let $x_1, x_2, \ldots, x_n$ be the coordinates of $x$ relative to $\left \langle {a_n} \right \rangle$.

Then for $i = 1,\ldots,n$ the map $f_i : G \to R$ defined by $f_i\left( x\right) = x_i$ is called the $i$-th coordinate function on $G$ relative to $\left \langle {a_n} \right \rangle$.