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Consider a rank-1 matrix composed by the outer product of two vectors: xy^T. Then make a symmetric one from it: reflect the right upper part onto the lower left one.

I am interested in inverting it. Can you please reference to an appropriate paper?

Does such a matrix have a special name? It would help for googling.


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Look for semi-separable matrix. The inverse of a tri-diagonal matrix is a semi-separable matrix with separable rank (of the off-diagonal blocks) being $1$. The inverse in your case is a tri-diagonal matrix. – user17762 Aug 30 '12 at 11:59
Thanks for "semi-separable", that's the name! – Konstantin Aug 30 '12 at 12:31

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