rsf2csf
Convert the real Schur form of a matrix to its complex Schur form.
[Tc,Qc]=rscf2csf(T,Q)
Inputs
T The first output of the function schur that returns the Schur form of a matrix.
Q The second output of the function schur that returns the Schur form of a matrix.
Outputs
Tc A possibly complex but strictly upper triangular matrix.
Qc A possibly complex unitary matrix.


Description
If the pair (T,Q) is computed from [T,Q]=schur(a) , the outputs of rsf2csf also satisfy Qc'*a*Qc=Tc . However, only the upper triangular part of Tc contains non-zero elements, whereas T may contain elements in the sub-diagoanl immediately below the main diagonal.


Example
>>a=[1 2 3 4 ; 10 12 15 23; 15 18 23 19; 18 25 123 19]
>>a
          1          2          3          4
         10         12         15         23
         15         18         23         19
         18         25        123         19

>>[T,Q]=schur(a)
>>//Note that T is upper triangular except for the nozero element T[4,3]
>>// in the lower triangular part. 
>>T
      85.2031     -13.3272      52.2308      -81.852
  2.3093e-014      -0.5539      -5.8584      16.1396
 -1.7764e-014 -6.2172e-015     -10.7226      35.6653
 -1.4211e-014  7.1054e-015      -0.8419     -18.9266

>>[Tc,Qc]=rsf2csf(T,Q)
>>// Note that Tc is strictly upper triangular.
>>Tc
Columns 1 through 3
      85.2031                      -13.3272                       51.0749 +    34.2306i   
            0                       -0.5539                       -6.7855 -     3.8394i   
 -1.7764e-014                  -6.2172e-015                      -14.8246 +     3.6335i   
 -1.4211e-014                   7.1054e-015                             0                 
Column 4
     -52.6288 +    53.6435i   
      11.0517 -    10.5774i   
       5.1466 -    35.4046i   
     -14.8246 -     3.6335i   

>>norm(Qc*Tc*Qc'-a)
       2.3559e-013