How Solve equation having Matrix parameters in Matlab

Question

I want to solve the following equation for X. All parameters in my equation are matrices:

( [A]' * [X] )+( [X] * [A] ) = -I

I =

     0         0         0         0
     0         0         0         0
     0         0    6.7955   -2.8529
     0         0   -2.8529    3.9426

and

[A] =

 -0.0038   -0.0011   -0.0012   -0.0012
 -0.0011   -0.0049   -0.0012   -0.0023
  1.0000       0         0        0
     0      1.0000       0        0

Answer 1

You can use sylvester :

>> sylvester(A', A, -I)

ans =

   1.0e+06 *

    2.2772   -1.4202    0.0071   -0.0045
   -1.4202    0.9749   -0.0043    0.0032
    0.0071   -0.0043    0.0011   -0.0005
   -0.0045    0.0032   -0.0005    0.0005