On 4 Nov 2003 at 13:14, Stephane DRAY wrote:
That the matrix is symmetric is sufficient to guarantee real
eigenvalues (proof is easy). I don't know about any general
conditions for asymmetric matrices, and doubt there are.
But in many structured situation you could be able to show similarity
with a symmetric matrix, which suffices. Also note that symmetry
doesn't need to be "visual" symmetry, it is enogh with symmetry
with respect to an inner product.
An example: Let A, B symmetric with B invertible .
Then B^{-1}A has real eigenvalues, since it is similar to a symmetric
matrix.
Kjetil Halvorsen
> Hello list,
>
> Sorry, these questions are not directly linked to R.
>
> If I consider an indefinte real matrix, I would like to know if the
> symmetry of the matrix is sufficient to say that their eigenvectors are real ?
> And what is the conditions to ensure that eigenvectors are real in the case
> of an asymmetric matrix (if some conditions exist)?
>
> Thanks in Advance,
> St�phane DRAY
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