Determinant function/Definition

Let ${\displaystyle {}V}$ be a vector space over a field ${\displaystyle {}K}$ of dimension ${\displaystyle {}n}$. A mapping

${\displaystyle \triangle \colon V^{n}\longrightarrow K}$

is called a determinant function if the following two conditions are fulfilled.

1. ${\displaystyle {}\triangle }$ is multilinear.
2. ${\displaystyle {}\triangle }$ is alternating.