Standard Basis Vectors of the Complex Coordinate Space

Let $n$ be a natural number, let $[n]$ be the initial segment determined by $n$, let $\mathbb{C}^{n}$ be the complex coordinate space, and let $k\in[n]$.

The $k$-th standard basis vector $e_{k}$ is the element of $\mathbb{C}^{n}$ whose $k$-th component is $1$ and whose $j$-th component is $0$ for every $j\in[n]$ with $j\ne k$.