decomplexification of a matrix

Hi, I have the following matrix

A= [5 10; 
   -1 -1]

This matrix has two complex eigenvalues e = 2 +- i

I would like to obtain a matrix

T=[a   -b;
   b   a]

using matlab.

manually the solution is

(-3   - i(1
 1)      0)

and

P=[-3 1;
    1 0];  
Pinv=[0 1; 
      1 3]

and

Pinv*A*P=[2  -1; 
          1   2]

as the matrix T.

But how can I do it using matlab?

My best regards, jim

Answer 1

[Image Analyst]

Just like you have it. Did you try:

A= [5 10;
   -1 -1]
P=[-3 1;
    1 0]
Pinv=[0 1;
      1 3]

T = Pinv*A*P

In the command window:

A =
     5    10 
    -1    -1
P =
    -3     1
     1     0
Pinv =
     0     1
     1     3
T =
     2    -1
     1     2

If so, isn't that what you want? Or did you run into problems?