Compute the inner product of two distinct vectors from the set of standard unit vectors (Definition SUV), say $\vect{e}_i$, $\vect{e}_j$, where $i\neq j$, \begin{align*} \innerproduct{\vect{e}_i}{\vect{e}_j}&= \conjugate{0}0+ \conjugate{0}0+\cdots+ \conjugate{1}0+\cdots+ \conjugate{0}0+\cdots+ \conjugate{0}1+\cdots+ \conjugate{0}0+ \conjugate{0}0\\ &=0(0)+0(0)+\cdots+1(0)+\cdots+0(1)+\cdots+0(0)+0(0)\\ &=0 \end{align*}
So the set $\set{\vectorlist{e}{m}}$ is an orthogonal set.