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Bunch–Nielsen–Sorensen formula : ウィキペディア英語版
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 and the outer product, v v^T, of vector v with itself.
==Statement==
Let \lambda_i denote the eigenvalues of A and \tilde\lambda_i denote the eigenvalues of the updated matrix \tilde A = A + v v^T. In the special case when A is diagonal, the eigenvectors \tilde q_i of \tilde A can be written
: (\tilde q_i)_k = \frac
where N_i is a number that makes the vector \tilde q_i normalized.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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