Adjoint of a matrix
This functionality does not run in MATLAB.
linalg::adjoint(A) computes the adjoint Adj(A) of the n×n matrix A. The adjoint matrix satisfies the equation , where In is the n×n identity matrix.
The component ring of A must be of category Cat::CommutativeRing.
We define a matrix over the rationals:
MatQ := Dom::Matrix(Dom::Rational): A := MatQ([[0, 2, 1], [2, 1, 0], [1, 0, 2]])
Then the adjoint matrix of A is given by:
Ad := linalg::adjoint(A)
We check the property of the adjoint matrix Ad mentioned above:
A * Ad = det(A)*MatQ::identity(3)
A square matrix of a domain of category Cat::Matrix
The adjoint of a square matrix A is the matrix whose (i, j)-th entry is the (j, i)-th cofactor of A.
The (j, i)-th cofactor of A is defined by , where Aij is the submatrix of A obtained from A by deleting the i-th row and j-th column.