Coordinate space

Description

Let $F$ be a field and let $n \ge 0$ be an integer. The coordinate space $F^n$ is the set of $n$-tuples $(x_1, \dots, x_n)$ with $x_i \in F$. It is a vector space over $F$ with the operations $$(x_1, \dots, x_n) + (y_1, \dots, y_n) = (x_1 + y_1, \dots, x_n + y_n), \qquad a(x_1, \dots, x_n) = (ax_1, \dots, ax_n).$$ Its zero vector is $(0, \dots, 0)$.