Determinant function/Definition

Determinant function

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

$\mathrm{△}:V^n⟶K$

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

1. $\mathrm{△}$ is multilinear.
2. $\mathrm{△}$ is alternating.