Definition SUV Standard Unit Vectors

Let $\vect{e}_j\in\complex{m}$, $1\leq j\leq m$ denote the column vectors defined by \begin{align*} \vectorentry{\vect{e}_j}{i} &= \begin{cases} 0&\text{if $i\neq j$}\\ 1&\text{if $i=j$} \end{cases} \end{align*}

Then the set \begin{align*} \set{\vectorlist{e}{m}}&=\setparts{\vect{e}_j}{1\leq j\leq m} \end{align*} is the set of standard unit vectors in $\complex{m}$.