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
denote the eigenvalues of
denote the eigenvalues of the updated matrix
In the special case when
is diagonal, the eigenvectors
can be written where
is a number that makes the vector
This formula can be derived from the Sherman–Morrison formula by examining the poles of
were studied by Golub.
[2] Numerical stability of the computation is studied by Gu and Eisenstat.