I have the following matrix , can i smiplify this further ?
$$B=(Z^TZ)^{-1} + (Z^TZ)^{-1}Z^T( I - P_z)^{-1}Z(Z^TZ)^{-1} $$
Where $Z$ is a (n x 1 ) vector, $I$ is the identity matrix and
$P_z$ is the projection matrix of Z So $P_Z = Z(Z^TZ)^{-1}Z^T$.
Can i simplify this further ? Since $(Z^TZ)^{-1}$ is in the both sides of the second term , i dont know how to factor it out.
Thank you.
Since $Z^TZ$ is a scalar, you can write $$B=(Z^TZ)^{-1}(I-(Z^TZ)^{-1}Z^T(I-P_z)^{-1}Z)$$