Let $\displaystyle A$ be a (nxn) matrix and $\displaystyle w$ be a n-column vector. Assume that $\displaystyle \sum_{i=0}^\infty A^i$ converges (geometric series). Is there a closed form expression for

$\displaystyle

\sum_{i=0}^\infty A^i w \left( A^i w)^T

$