CofactorMatrix
Computes the cofactor matrix of a square matrix.
Syntax
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CofactorMatrix(A)-
Ais a square matrix
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Description
If A is a square matrix, then CofactorMatrix(A) returns the cofactor matrix of A, that is, the matrix of all cofactors of A. In other words,
CofactorMatrix(A) = = matrix(compute(cofactor(A, i, j), i, 1, size(A).rows, j, 1, size(A).cols))
= matrix(compute((−1)^(i + j) ⋅ minor(A, i, j),
i, 1, size(A).rows, j, 1, size(A).cols))
= matrix(compute((−1)^(i + j) ⋅ det(SubmatrixByRemoval(A, i, j)),
i, 1, size(A).rows, j, 1, size(A).cols)).
Examples
A ≔ ❨❨4, 1, 2, 3❩, ❨6, 1, 2, 3❩, ❨7, 6, 5, 0❩, ❨1, 2, 1, 6❩❩
⎛4 1 2 3⎞ ⎜6 1 2 3⎟ ⎜7 6 5 0⎟ ⎝1 2 1 6⎠
CofactorMatrix(A)
⎛ −54 −102 198 10⎞ ⎜ 54 42 −126 −2⎟ ⎜ 0 18 0 −6⎟ ⎝ 0 30 −36 14⎠