Thread: matrix algebra

for the square matrix A can
(I + A)^-1 be expanded or simplified. is it true (I + A)^-1 = A^-1 - I
where I is the identity matrix
thanks to anyone who can help

Originally Posted by smiler

for the square matrix A can
(I + A)^-1 be expanded or simplified. is it true (I + A)^-1 = A^-1 - I
where I is the identity matrix
thanks to anyone who can help

No, it is not true. (It's not even true for scalars.)
Consider:

(I just randomly selected numbers here. It is not a "special" case.)

You'll see that it doesn't work out.

-Dan