Re: minors and cofactors

[Dirk Laurie]

Thanks to David Clark for a fascinating question.  I keep getting
new thoughts after having posted two answers, but this is the last
one.

There is a fully satisfactory way of calculating the cofactor matrix
that requires no rank decision.

Calculate the SVD  A=U*S*V'.
Then det(A)=det(U)*det(S)*det(V')
and  inv(A)=V*inv(S)*U'.
Hence  inv(A)*det(A) = (det(V')*V) * (det(S)*inv(S)) * (det(U)*U')
The middle factor can be calculated by replacing each diagonal term
be the product of the others.

Dirk