Let B, A, and e be square matrices with e small, and define
where I is the Identity Matrix. Then the inverse of
This can be seen by multiplying
Note that if we instead let
, and look for an inverse of the form
, we obtain
In order to eliminate the
term, we require
. However, then
so there can be no inverse of this form.
The exact inverse of
can be found as follows.
Using a general Matrix Inverse identity then gives
© 1996-9 Eric W. Weisstein