Thread: Symmetric 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

Hello,

Originally Posted by Chris0724

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

This is logic !



But this is different from .

This is the converse of the implication. And is not always true.

Originally Posted by Moo

Hello,

This is logic !



But this is different from .

This is the converse of the implication. And is not always true.

So in short, i will always get a Real eigenvalues from a symmetric matrix but Real eigenvalues does not meant that the matrix must be symmetric?

Thanks!

Originally Posted by Chris0724

So in short, i will always get a Real eigenvalues from a symmetric matrix but Real eigenvalues does not meant that the matrix must be symmetric?

Thanks!

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