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Math Help - Closed form solution of matrix series?

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    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
    <br />
\sum_{i=0}^\infty A^i w \left( A^i w)^T<br />
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    MHF Contributor Bruno J.'s Avatar
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    Quote Originally Posted by martinVT View Post
    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
    <br />
\sum_{i=0}^\infty A^i w \left( A^i w)^T<br />
    Nice question. Try looking at the partial sum S_n, and find an expression for AS_nA^T...
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