Adjugate (adjoint) of a Square Matrix

Calculates the adjugate (adjoint) matrix for a square matrix.

For any n x n matrix, A, with real or complex-valued elements, whether singular or not, its adjugate (also known as its adjoint) matrix, adj(A), is calculated. The svd function is called on to find [u,s,v] = svd(A), and the identity adj(A) = det(u*v')*v*adj(s)*u', which holds even if A is singular, is computed. Tests have shown that the accuracy remains good even up to values of n as large as 32 provided adj(A) does not overflow or underflow matlab's double precision capacity. The definition of the adjugate (adjoint) of matrix A is a matrix in which its element in the i-th row and j-th column is the cofactor of the element of A in the j-th row and i-th column.