Pseudo-Hermiticity

[ChiYung Yam <yamcy^at^yangtze.hku.hk>]

 Dear all,
 I found from the literature that a matrix will have all real
 eigenvalues if it is pseudo-hermitian. For pseudo-hermitian, it means
 \etta A \etta^{-1} = A^{daggar}
 where \etta is a hermitian and invertible matrix and A is the matrix we
 are interested in.
 However, if given a matrix with complex eigenvalues, how can I make it
 pseudo-hermitian with minimal changes to the matrix elements? Is there
 any simple way to do it?
 Thank you very much
 Best regards,
 Yam