## 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 $\Lambda,Q$.

$Q$ $\Lambda$ $Q^T$ $A$
 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
=
 * * * * * * * * * * * * * * * * * * * * * * * * *
 $c=$ $s=$ $\mathrm{sqsum}(\Lambda)=$* $\mathrm{diagss}(\Lambda)=$* diff =*