Bunch–Nielsen–Sorensen formula

In mathematics, in particular linear algebra, the Bunch–Nielsen–Sorensen formula, named after James R. Bunch, Christopher P. Nielsen and Danny C. Sorensen, expresses the eigenvectors of the sum of a symmetric matrix A {\displaystyle A} and the outer product, v v T {\displaystyle vv^{T}} , of vector v {\displaystyle v} with itself. == Statement == Let λ i {\displaystyle \lambda _{i}} denote the eigenvalues of A {\displaystyle A} and λ ~ i {\displaystyle {\tilde {\lambda }}_{i}} denote the eigenvalues of the updated matrix A ~ = A + v v T {\displaystyle {\tilde {A}}=A+vv^{T}} .

Source: Wikipedia — Bunch–Nielsen–Sorensen formula (CC BY-SA 4.0)