Thread: Closed form solution of matrix series?

1. Closed form solution of matrix series?

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

2. Originally Posted by martinVT
Let $A$ be a (nxn) matrix and $w$ be a n-column vector. Assume that $\sum_{i=0}^\infty A^i$ converges (geometric series). Is there a closed form expression for
$
\sum_{i=0}^\infty A^i w \left( A^i w)^T
$
Nice question. Try looking at the partial sum $S_n$, and find an expression for $AS_nA^T$...