Algebra/Determinants

The determinant function is a multilinear and anti-symmetric mapping given by

$\sum _{\sigma \in S}(sgn(\sigma )\prod _{j=1}^n{a}_{j\sigma (j)})det(e_1,e_2,\cdots ,e_n).$

It is unique determined by $det(e_1,e_2,\cdots ,e_n)$.