Find a transformation matrix [T] to get a specific matrix form.

May 2017
2
0
UK
Hi geniuses.
I desperately need urgent help, and I will be very grateful if someone (Nod) could help me.

My problem (Headbang) 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
=
[a, b+jc;
-b-jc, f ].

where [ T ]*[M]*[ T ]conjTr =[N]

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 has a special form "detectable" like hermitian, symmetric, or per symmetric......
Thank you,
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
Frankly, I have no idea what you are doing here. Your very first assertion, that matrix [M] is symmetric, is clearly wrong. [M] is the sum of a diagonal and an anti symmetric matrix.
 
May 2017
2
0
UK
I admit I lost focus when I wrote. yes [M] is an anti symmetric matrix.

The 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 Anti-symetric

Now let define
N=
[d+je, 0, 0;
0, a, b+jc;
0, -b-jc, f ]

where the subMatrix
=
[a, b+jc;
-b-jc, f ].

where [ T ]*[M]*[ T ]conjTr =[N]

has a special form as in this exemple is anti-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 has a special form "detectable" like hermitian, symmetric, or per symmetric......
Thank you,