Determinante/Leibnizformel/Fakt

Leibniz-Formel für die Determinante

Für die Determinante einer ${}n\times n$ -Matrix

{}M=(a_{ij})_{ij}\,

gilt

${}\det M=\sum _{\pi \in S_{n}}\operatorname {sgn} (\pi )a_{1\pi (1)}\cdots a_{n\pi (n)}\,.$

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