The theorem state that the eigenvalues of a symmetric are real.
[ 3 4 | has real eigenvalues 1 & 5 (verified) but why not symmetric?
| 1 3 |
Rgds
Exactly !
The symmetry of a matrix is a sufficient but not necessary condition. If it was, you would have an equivalence, not an implication
Necessary and sufficient condition - Wikipedia, the free encyclopedia