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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.

Thanks!

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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.2012-08-30
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    Thanks for "semi-separable", that's the name!2012-08-30

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