ヤコビ法 (固有値問題)
{\displaystyle U_{1}:={\begin{bmatrix}1&\cdots &0&\cdots &0&\cdots &0\\\vdots &\ddots &\vdots &&\vdots &&\vdots \\0&\cdots &\cos(\theta )&\cdots &\sin(\theta )&\cdots &0\\\vdots &&\vdots &\ddots &\vdots &&\vdots \\0&\cdots &-\sin(\theta )&\cdots &\cos(\theta )&\cdots &0\\\vdots &&\vdots &&\vdots &\ddots &\vdots \\0&\cdots &0&\cdots &0&\cdots &1\end{bmatrix}},\quad u_{pp}=u_{qq}=\cos(\theta ),\quad u_{pq}=\sin(\theta ),\quad u_{qp}=-\sin(\theta ).}
tan  ( 2 θ ) = − 2 a p q a p p − a q q , − π / 4 ≤ θ ≤ π / 4. {\displaystyle \tan(2\theta )={\frac {-2a_{pq}}{a_{pp}-a_{qq}}},\quad -\pi /4\leq \theta \leq \pi /4.}
このとき、非対角要素のうちで絶対値最大な要素 a p q {\displaystyle a_{pq}} に対して