Hi geniuses.

I desperately need urgent help, and I will be very grateful if someone could help me.

My problem is how to find a transformation matrix [T] of a matrix [M], as specified in the example below:

Let

[M]=

[a, b+jc, d+je;

-b-jc, f, b+jc;

-d-je, -b-jc, a ]

As we notice that [M] is symetric

Now let define

N=

[d+je, 0, 0;

0, a, b+jc;

0, -b-jc, f ]

where the subMatrix

[S]=

[a, b+jc;

-b-jc, f ].

where [ T ]*[M]*[ T ]^{conjTr }=[N]

[S] has a special form as in this exemple is symetric , but could be hermitian, anti symetric, centrosymetric........etc

The purpose, is to get the form of N. Without losing information. And the sub matrix [S] has a special form "detectable" like hermitian, symmetric, or per symmetric......

Thank you,