Leibniz formula for determinants

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In algebra, the Leibniz formula, named in honor of Gottfried Leibniz, expresses the determinant of a square matrix in terms of permutations of the matrix elements. If A {\displaystyle A} is an n × n {\displaystyle n\times n} matrix, where a i j {\displaystyle a_{ij}} is the entry in the i {\displaystyle i} -th row and j {\displaystyle j} -th column of A {\displaystyle A} , the formula is det ( A ) = ∑ τ ∈ S n sgn ⁡...

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