schur
The Schur decomposition of a square matrix.
(T, Q)=schur(a)
Inputs
a Any square matrix.
Outputs
u A quasi-upper triangle matrix.
v A unitary matrix (i.e. Q'Q=eye(size(a)) ).


Description
The outputs of Schur satisfy Q'*a*Q=T. The matrix T is upper traiangle except that in many cases there may be non-zero elements in the sub-diagonal 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

>>Q
      -0.0624       0.7481      -0.6027      -0.2705
       -0.354      -0.6354      -0.6307      -0.2704
      -0.3781       0.0849      -0.2533       0.8864
      -0.8531       0.1714       0.4181      -0.2608

>>norm(Q*T*Q'-a)
       2.2649e-013