| context | $n\in \mathbb N$ |
| context | $R$ … abelian ring |
| definiendum | $ \mathrm{det}_n:\mathrm{SquareMatrix}(n,R)\to R$ |
| definiendum | $ \mathrm{det}_n(A):=\sum_{j_1,\dots,j_n}^n\varepsilon_{j_1,\dots,j_n}\cdot \prod_{k=1}^n A_{k,j_k}$ |
This function concides with the implicitly defined determinant of Determinant, if the matrices are taken to be linear operators in the usual way.
Wikipedia: Leibniz formula for determinants