===== Leibniz formula for determinants =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $n\in \mathbb N$ | 
| @#55CCEE: context     | @#55CCEE: $R$ ... abelian ring | 

| @#FFBB00: definiendum | @#FFBB00: $ \mathrm{det}_n:\mathrm{SquareMatrix}(n,R)\to R$ |
| @#FFBB00: definiendum | @#FFBB00: $ \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}$ |

==== Discussion ====
This function concides with the implicitly defined determinant of [[Determinant]], if the matrices are taken to be linear operators in the usual way.
=== Reference ===
Wikipedia: [[http://en.wikipedia.org/wiki/Leibniz_formula_for_determinants|Leibniz formula for determinants]]
==== Parents ====
=== Context ===
[[Matrix ring]],
[[Determinant via multilinear functionals]],
[[Infinite series]]