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- Laplace_expansion abstract "In linear algebra, the Laplace expansion, named after Pierre-Simon Laplace, also called cofactor expansion, is an expression for the determinant |B| ofan n × n square matrix B that is a weighted sum of the determinants of n sub-matrices of B, each of size (n−1) × (n−1). The Laplace expansion is of theoretical interest as one of several ways to view the determinant, as well as of practical use in determinant computation.The i, j cofactor of B is the scalar Cij defined bywhere Mij is the i, j minor matrix of B, that is, the determinant of the (n–1) × (n–1) matrix that results from deleting the i-th row and the j-th column of B.Then the Laplace expansion is given by the followingTheorem. Suppose B = (bij) is an n × n matrix and fix any i, j ∈ {1, 2, ..., n}.Then its determinant |B| is given by:".
- Laplace_expansion wikiPageExternalLink LaplaceExpansion2.html.
- Laplace_expansion wikiPageID "3506553".
- Laplace_expansion wikiPageRevisionID "594701822".
- Laplace_expansion hasPhotoCollection Laplace_expansion.
- Laplace_expansion subject Category:Articles_containing_proofs.
- Laplace_expansion subject Category:Determinants.
- Laplace_expansion subject Category:Matrix_theory.
- Laplace_expansion type Abstraction100002137.
- Laplace_expansion type Cognition100023271.
- Laplace_expansion type CognitiveFactor105686481.
- Laplace_expansion type Determinant105692419.
- Laplace_expansion type Determinants.
- Laplace_expansion type PsychologicalFeature100023100.
- Laplace_expansion comment "In linear algebra, the Laplace expansion, named after Pierre-Simon Laplace, also called cofactor expansion, is an expression for the determinant |B| ofan n × n square matrix B that is a weighted sum of the determinants of n sub-matrices of B, each of size (n−1) × (n−1).".
- Laplace_expansion label "Laplace expansion".
- Laplace_expansion label "Rozwinięcie Laplace’a".
- Laplace_expansion label "Teorema de Laplace".
- Laplace_expansion label "Teorema de Laplace".
- Laplace_expansion label "Teorema di Laplace".
- Laplace_expansion label "Теорема Лапласа".
- Laplace_expansion label "拉普拉斯展开".
- Laplace_expansion sameAs Teorema_de_Laplace.
- Laplace_expansion sameAs Teorema_di_Laplace.
- Laplace_expansion sameAs Rozwinięcie_Laplace’a.
- Laplace_expansion sameAs Teorema_de_Laplace.
- Laplace_expansion sameAs m.09h71r.
- Laplace_expansion sameAs Q2044612.
- Laplace_expansion sameAs Q2044612.
- Laplace_expansion sameAs Laplace_expansion.
- Laplace_expansion wasDerivedFrom Laplace_expansion?oldid=594701822.
- Laplace_expansion isPrimaryTopicOf Laplace_expansion.