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In linear algebra, the Laplace expansion, named after Pierre-Simon Laplace, also called cofactor expansion, is an expression of the determinant of an n × n-matrix B as a weighted sum of minors, which are the determinants of some (n − 1) × (n − 1)-submatrices of B.
The cofactors feature prominently in Laplace's formula for the expansion of determinants, which is a method of computing larger determinants in terms of smaller ones. Given an n × n matrix A = ( a ij ) , the determinant of A , denoted det( A ) , can be written as the sum of the cofactors of any row or column of the matrix multiplied by the ...
the positive and negative cofactors of ... There is a similar decomposition corresponding to an expansion about = (negative Davio expansion): = ¯. Repeated ...
In linear algebra, the adjugate or classical adjoint of a square matrix A, adj(A), is the transpose of its cofactor matrix. [1] [2] It is occasionally known as adjunct matrix, [3] [4] or "adjoint", [5] though that normally refers to a different concept, the adjoint operator which for a matrix is the conjugate transpose.
Cofactor may also refer to: Cofactor (biochemistry), a substance that needs to be present in addition to an enzyme for a certain reaction to be catalysed; A domain parameter in elliptic curve cryptography, defined as the ratio between the order of a group and that of the subgroup; Cofactor (linear algebra), the signed minor of a matrix
Pages for logged out editors learn more. Contributions; Talk; Cofactor expansion
Writing the transpose of the matrix of cofactors, known as an adjugate matrix, can also be an efficient way to calculate the inverse of small matrices, but this recursive method is inefficient for large matrices. To determine the inverse, we calculate a matrix of cofactors:
Rule of Sarrus: The determinant of the three columns on the left is the sum of the products along the down-right diagonals minus the sum of the products along the up-right diagonals.