Let B, A, and e be square matrices with e small, and define
|
(1) |
where I is the Identity Matrix. Then the inverse of
is approximately
|
(2) |
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
so there can be no inverse of this form.
The exact inverse of
can be found as follows.
|
(5) |
so
|
(6) |
Using a general Matrix Inverse identity then gives
|
(7) |
© 1996-9 Eric W. Weisstein
1999-05-26