Leibniz formula for determinants
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 is an n×n matrix, where ai,j is the entry in the ith row and jth column of A, the formula is where sgn is the sign function of permutations in the permutation group Sn, which returns +1 and −1 for even and odd permutations, respectively. Another common notation used for the formula is in terms of the Levi-Civita symbol and makes use of the Einstein summation notation, where it becomes which may be more familiar to physicists.
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Leibniz formula for determinants
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 is an n×n matrix, where ai,j is the entry in the ith row and jth column of A, the formula is where sgn is the sign function of permutations in the permutation group Sn, which returns +1 and −1 for even and odd permutations, respectively. Another common notation used for the formula is in terms of the Levi-Civita symbol and makes use of the Einstein summation notation, where it becomes which may be more familiar to physicists.
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Determinant&oldid=12692
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En álgebra lineal, la fórmula ...... la fórmula de Leibniz requiere
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In algebra, the Leibniz formul ...... e more familiar to physicists.
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Fórmula de Leibniz para el cálculo de determinantes
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Leibniz formula for determinants
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