## Eigenvalue Problem for symmetric matrices: The Jacobi Method

### The parameters

Matrix dimension = 5. Precision = 2 digits. Magnitude of matrix entries = 100.

### The diagonalization

 1 Determine $i,j$ ($i\neq j$) such that $|a_{ij}|$ is maximal. 2 Compute $c,s$. 3 Recalculate $A,Q$.

$Q^t$$A$$Q$$B$
 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1
 * * * * * * * * * * * * * * * * * * * * * * * * *
 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1
=
 * * * * * * * * * * * * * * * * * * * * * * * * *
 $\sum_{i\neq j}a_{ij}^2=$* $c=$ $\sum_{i}a_{ii}^2=$* $s=$

Copyright by © Gábor P. Nagy, 2013.