The projection of \(\RNrSpc{m}\) onto the \(i\)-th coordinate is the function

\[ \PrjctnOnto{i}\from \RNrSpc{m} \longrightarrow \RNr,\qquad \PrjctnOntoOfCoord{i}{(x_1,\dots ,x_m)} = \underset{\longleftarrow\quad\ i\quad\ \longrightarrow}{[0\ \dots\ 1\ \dots\ 0]}\left[\begin{array}{c} x_1 \\ \vdots \\ x_i\\ \vdots \\ x_n\end{array}\right] =x_i \]