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- Leibniz_formula_for_determinants abstract "In algebra, the Leibniz formula expresses the determinant of a square matrix in terms of permutations of the matrix elements. Named in honor of Gottfried Leibniz, the formula isfor an n×n matrix, 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 becomeswhich may be more familiar to physicists.Directly evaluating the Leibniz formula from the definition requires operations in general—that is, a number of operations asymptotically proportional to n factorial—because n! is the number of order-n permutations. This is impractically difficult for large n. Instead, the determinant can be evaluated in O(n3) operations by forming the LU decomposition (typically via Gaussian elimination or similar methods), in which case and the determinants of the triangular matrices L and U are simply the products of their diagonal entries. (In practical applications of numerical linear algebra, however, explicit computation of the determinant is rarely required.) See, for example, Trefethen and Bau (1997).".
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- Leibniz_formula_for_determinants hasPhotoCollection Leibniz_formula_for_determinants.
- Leibniz_formula_for_determinants id "Determinant&oldid=12692".
- Leibniz_formula_for_determinants title "Determinant".
- Leibniz_formula_for_determinants subject Category:Articles_containing_proofs.
- Leibniz_formula_for_determinants subject Category:Determinants.
- Leibniz_formula_for_determinants subject Category:Gottfried_Leibniz.
- Leibniz_formula_for_determinants subject Category:Linear_algebra.
- Leibniz_formula_for_determinants type Abstraction100002137.
- Leibniz_formula_for_determinants type Cognition100023271.
- Leibniz_formula_for_determinants type CognitiveFactor105686481.
- Leibniz_formula_for_determinants type Determinant105692419.
- Leibniz_formula_for_determinants type Determinants.
- Leibniz_formula_for_determinants type PsychologicalFeature100023100.
- Leibniz_formula_for_determinants comment "In algebra, the Leibniz formula expresses the determinant of a square matrix in terms of permutations of the matrix elements.".
- Leibniz_formula_for_determinants label "Fórmula de Leibniz para el cálculo de determinantes".
- Leibniz_formula_for_determinants label "Leibniz formula for determinants".
- Leibniz_formula_for_determinants sameAs Fórmula_de_Leibniz_para_el_cálculo_de_determinantes.
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- Leibniz_formula_for_determinants sameAs Q538557.
- Leibniz_formula_for_determinants sameAs Q538557.
- Leibniz_formula_for_determinants sameAs Leibniz_formula_for_determinants.
- Leibniz_formula_for_determinants wasDerivedFrom Leibniz_formula_for_determinants?oldid=597256397.
- Leibniz_formula_for_determinants isPrimaryTopicOf Leibniz_formula_for_determinants.