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

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- Sep 22nd 2008, 10:20 PMChris0724Symmetric Matrix
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 - Sep 22nd 2008, 10:57 PMMoo
Hello,

This is logic ! :)

$\displaystyle \text{Symmetric matrix } \implies \text{ Real eigenvalues}$

But this is**different**from $\displaystyle \text{Real eigenvalues } \implies \text{ Symmetric matrix}$.

This is the converse of the implication. And is not always true. - Sep 22nd 2008, 11:08 PMChris0724
- Sep 22nd 2008, 11:11 PMMoo
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