In mathematics, in particular linear algebra, the Bunch–Nielsen–Sorensen formula,[1] named after James R. Bunch, Christopher P. Nielsen and Danny C. Sorensen, expresses the eigenvectors of the sum of a symmetric matrix and the outer product, , of vector with itself.
Let denote the eigenvalues of and denote the eigenvalues of the updated matrix . In the special case when is diagonal, the eigenvectors of can be written
where is a number that makes the vector normalized.
This formula can be derived from the Sherman–Morrison formula by examining the poles of .
The eigenvalues of were studied by Golub.[2]
Numerical stability of the computation is studied by Gu and Eisenstat.[3]