Example

> root2on2 = 
 root2on2 =
    0.707
> M = [ sqrt(2)/2, sqrt(2)/2, 0; sqrt(2)/2, sqrt(2)/2, 0; 0,0,1]
 M =
    0.707      0.707          0  
    0.707      0.707          0  
        0          0          1  
> R = schur(M)
 R =
   t            z            
> R.t
     1.41          0          0  
        0  -1.11e-16          0  
        0          0          1  
> R.z
    0.707     -0.707          0  
    0.707      0.707          0  
        0          0          1  
> R.z*R.t*R.z'
    0.707      0.707          0  
    0.707      0.707          0  
        0          0          1  
> Comp = 10*(rand(3,3)+rand(3,3)+1j)
 Comp =
 matrix columns 1 thru 3
             0.935 + 10i              4.88 + 10i              3.83 + 10i
              11.5 + 10i              13.4 + 10i              19.5 + 10i
              11.4 + 10i              5.25 + 10i              8.41 + 10i

> SchRes = schur(Comp)
 SchRes =
   t            z            
> Comp - SchRes.z*SchRes.t*SchRes.z'
 matrix columns 1 thru 3
   -5.33e-15 - 1.42e-14i   -1.42e-14 - 3.55e-15i      -4e-15 - 5.33e-15i
   -1.78e-15 - 1.95e-14i    3.55e-15 + 3.55e-15i    3.55e-15 - 1.42e-14i
   -8.88e-15 - 1.07e-14i   -6.22e-15 + 5.33e-15i    3.55e-15 - 1.07e-14i