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The Eigenvectors in the Jacobi Method

Eventually we end up with a matrix D, which is diagonal to requested precision. The obtained transformation is:

\begin{displaymath}\boldsymbol{D} = \boldsymbol{V}^T\cdot\boldsymbol{A}\cdot\boldsymbol{V}
\end{displaymath} (3.35)


\begin{displaymath}\boldsymbol{V} = \boldsymbol{P}_1\cdot\boldsymbol{P}_2\cdot\boldsymbol{P}_3
\end{displaymath} (3.36)

Given matrix V we can compute the new matrix V'as follows:
v'rs = $\displaystyle v_{rs} \qquad \hbox{for} \qquad s\neq p, s\neq q$ (3.37)
v'rp = $\displaystyle cv_{rp} - s v_{rq} = v_{rp}
- s \left(v_{rq} + \tau v_{rp}\right),$ (3.38)
v'rq = $\displaystyle c v_{rq} + s v_{rp} = v_{rq}
+ s \left(v_{rp} - \tau v_{rq}\right)$ (3.39)

Zdzislaw Meglicki