Dear all,

I have an exercise which asks me to prove the following;

Let A be a non-singular matrix with transpose $\displaystyle A^T $ and inverse $\displaystyle A^{-1} $

Let b be a vector with transpose $\displaystyle b^T $.

Prove that for $\displaystyle b^T A^{-1} b $ =//not equal to//= $\displaystyle -1 $

$\displaystyle (A + b b^T)^{-1} = A^{-1} - (A^{-1} b b^T A^{-1})/(1+b^T A^{-1} b) $

Regards,

Reinout