Example

> a = rand(3,3)
 a =
    0.341      0.455      0.188  
    0.623     0.0178      0.946  
    0.182      0.071      0.799  
> b = rand(3,3)
 b =
    0.369      0.481      0.931  
    0.895      0.791       0.98  
    0.836      0.733      0.195  
> c = rand(3,3)
 c =
    0.459       0.46      0.749  
   0.0589      0.225      0.385  
    0.281      0.957      0.642  
> ResSylv = lyap(a,b,c)
 ResSylv =
   -0.804      0.868      -1.24  
    0.583     0.0114     -0.375  
     0.55     -0.825    -0.0942 
> a*ResSylv+ResSylv*b + c
 4.44e-16   8.88e-16   1.44e-15  
 5.55e-17  -1.11e-16   6.66e-16  
 2.22e-16          0   2.22e-16  
> ResLyap = lyap(a,,c)
 ResLyap =
    -3.75       7.11     -0.916  
    -3.07       2.15       1.22  
     2.29       -4.2     -0.427  
> a*ResLyap+ResLyap*a' + c
        0   8.88e-16   2.55e-15  
 1.94e-15  -2.39e-15   1.11e-16  
-1.11e-15  -1.11e-16  -1.33e-15