I have an exercise which asks me to prove the following;
Let A be a non-singular matrix with transpose A' and inverse inv(A)
Let b be a vector with transpose b'.
Prove that for b' A b =//not equal to//= -1
inv( A + b b' ) = inv(A) - inv(A) b b' inv(A) / ( 1 + b inv(A) b)
I tried to give the easiest notation possible and hope you can help me.
p.s. I attached an image to clarify the equation.