show/hide this revision's text 3 edited body; edited title

is there any effective efficient way to compute the follow matrix equations easily

Let $A$ and $D$ are $n\times n$ digonal diagnal matrices, and $B$ is an $n\times n$ orthogonal matrix. Is there any effective efficient way to compute the follow matrix equations easily?

$\sum_{i=0}^{k} A^i \cdot B^T \cdot D \cdot B \cdot A^i$

show/hide this revision's text 2 deleted 5 characters in body

Let $A$ and $D$ are $n\times n$ digonal matrices, and $B$ is an $n\times n$ orthogonal matrix. Is there any effective way to compute the follow matrix equations easily?

$\sum_{i=0}^{\infty} \sum_{i=0}^{k} A^i \cdot B^T \cdot D \cdot B \cdot A^i$

show/hide this revision's text 1

is there any effective way to compute the follow matrix equations easily

Let $A$ and $D$ are $n\times n$ digonal matrices, and $B$ is an $n\times n$ orthogonal matrix. Is there any effective way to compute the follow matrix equations easily?

$\sum_{i=0}^{\infty} A^i \cdot B^T \cdot D \cdot B \cdot A^i$