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I have an expression of the below form:

$$\sum_{i=1}^k (A_i+B)^{-1}=0$$ where $\{A_i\}_{i\in \{1,...k\}}$ are a set of known square symmetric invertible matrices and $B$ is an unknown square symmetric invertible matrix.

I wish to rearrange the above for $B$. How can I do this? It seems as though there must be a simple way but I cannot see one.

JDoe2
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  • if sums $A_i + B$ are invertible then this question may help you https://math.stackexchange.com/questions/17776/inverse-of-the-sum-of-matrices – oskarryn Jul 24 '20 at 17:31
  • Thank you - I don't see any direct way this can help though. I just can't seem to rearrange it in terms of A. – JDoe2 Jul 25 '20 at 22:12

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