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leibniz_formula_for_determinants [2013/09/17 23:22]
nikolaj
leibniz_formula_for_determinants [2014/03/21 11:11]
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-===== Leibniz formula for determinants ===== 
-==== Definition ==== 
-| @#88DDEE: $n\in \mathbb N$ |  
-| @#88DDEE: $R$ ... abelian ring |  
  
-| @#FFBB00: $ \mathrm{det}_n:​\mathrm{SquareMatrix}(n,​R)\to R$ | 
-| @#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}$ | 
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-==== 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 ==== 
-=== Requirements === 
-[[Matrix ring]] 
-=== Requirements === 
-[[Determinant via multilinear functionals]],​ 
-[[Infinite series]] 
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