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I am searching for an explicit expression or at least an efficient way to compute the inverse of $U+\Lambda$ where $U$ orthonormal and $\Lambda$ is diagonal. My attempts so far were very unfruitful.

Thanks a lot.

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The inverse of an orthonormal matrix is it's transpose. The inverse of a diagonal matrix is just the reciprocals of it's diagonal entries. The inverse of a sum is the sum of the inverses with some extra garbage, see here: jstor.org/stable/2690437 –  noobProgrammer Apr 2 '13 at 15:23
    
Thanks for the hint, but this applies only to rank one $\Lambda$. If I have a full rank diagonal matrix, I need to do $n$ recursions and do not gain anything. –  fabee Apr 4 '13 at 7:09
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