AdjugateMatrix
Computes the adjugate matrix (classical adjoint) of a square matrix.
Syntax
-
AdjugateMatrix(A)-
Ais a square matrix
-
Description
If A is a square matrix, then AdjugateMatrix(A) returns the adjugate matrix of A, that is, the transpose of the cofactor matrix of A. In other words,
AdjugateMatrix(A) =
= transpose(matrix(compute(cofactor(A, i, j),
i, 1, size(A).rows, j, 1, size(A).cols)))
= transpose(matrix(compute((−1)^(i + j) ⋅ minor(A, i, j),
i, 1, size(A).rows, j, 1, size(A).cols)))
= transpose(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⎠
adj ≔ AdjugateMatrix(A)
⎛ −54 54 0 0⎞ ⎜−102 42 18 30⎟ ⎜ 198 −126 0 −36⎟ ⎝ 10 −2 −6 14⎠
defuzz(A⋅adj)
⎛108 0 0 0⎞ ⎜ 0 108 0 0⎟ ⎜ 0 0 108 0⎟ ⎝ 0 0 0 108⎠
det(A)
108