Although my matrix III is symmetric, but not Hermitian, it is possible to convert it into the following matrix by simple row & column swaps: |a b' c' 0 | |b a' 0 c'| |c 0 a' b'| |0 c b a | If we're willing to give up integrality, we can always rotate the triangle so that the "a" side is parallel to the real axis, i.e., without loss of generality, we can make the "a" vector real. In this case, a=a', so the above matrix _is_ Hermitian. (I don't know of what use this is, however!) At 11:02 PM 6/29/2012, Pacher Christoph wrote:

Henry Baker wrote:

...

Matrix III is also a rare example of a _symmetric_ complex matrix that is _not Hermitian_.

Isn't a symmetric matrix A Hermitian iff A is real symmetric ?!

Christoph