Look at these examples. Then you decide.
Hi,
I was wondering if there was a relation between
det(A+B) and det(A) and det(B)
where A and B are n by n matrices.
Also, I was wondering what the reation between
det(A-B) and det(A) and det(B).
Thanks for any help.
I don't know if a relation is supposed to exist by the way...
There is no such relationship. To demonstrate this one need only find
matrices A, A', B, B' such that det(A)=det(A'), and det(B)=det(B') and
det(A+B) != det(A'+B'). Which with a bit of trial and error is easy enough
to do.
This demonstrates that there is no function f, such that:
f(det(A),det(B))=det(A+B).
(This is a stonger statement than IPH's that there is no simple relationship
between the determinants of two matrices and the determinant of the sum
of the matrices).
RonL