test
echo on
a=[1 2;3 6]

a =

     1     2
     3     6

[u,t]=schur(a)

u =

   -0.8944   -0.4472
    0.4472   -0.8944


t =

     0    -1
     0     7

norm(u'*u-eye(2))

ans =

   1.1102e-16


n=3

n =

     3

a1=round(10*randn(n)+i*10*randn(n))

a1 =

 -22.0000 -10.0000i   6.0000             6.0000 -19.0000i
  -1.0000             5.0000 - 3.0000i  -6.0000 + 4.0000i
 -10.0000            17.0000 +11.0000i   4.0000 + 9.0000i

[u1,t1]=schur(a1)

u1 =

   0.0462 - 0.9682i  -0.2278 - 0.0025i  -0.0322 - 0.0861i
  -0.0659 - 0.0300i   0.2954 + 0.0548i   0.6268 - 0.7153i
  -0.1274 - 0.1972i   0.7033 - 0.6027i   0.0331 + 0.2933i


t1 =

 -23.3303 -15.0039i  10.1569 + 0.4105i   0.0790 +13.0826i
        0             6.0855 +19.6916i  10.6361 + 5.9732i
        0                  0             4.2448 - 8.6877i

u1'*u1

ans =

   1.0000 + 0.0000i   0.0000 + 0.0000i  -0.0000 + 0.0000i
   0.0000 - 0.0000i   1.0000            -0.0000 - 0.0000i
  -0.0000            -0.0000 + 0.0000i   1.0000 - 0.0000i

norm(u1'*u1-eye(n))

ans =

   1.3467e-15


n=5

n =

     5

d2=round(10*randn(n,1));
p=randn(n);
a2=p*diag(d2)*inv(p);
[u2,t2]=schur(a2)

u2 =

   -0.4946   -0.6708    0.1708    0.2537   -0.4603
   -0.5824    0.0707    0.4488   -0.0292    0.6734
    0.6141   -0.4212    0.6454   -0.0947    0.1412
   -0.1313   -0.3285   -0.2301   -0.9059    0.0350
   -0.1473    0.5096    0.5477   -0.3243   -0.5599


t2 =

    0.0000   -4.8681    1.6250   -3.0532 -104.9332
         0    6.0000    0.0000    0.1478   -4.3439
         0   -0.0000    6.0000   -0.3519   -2.9825
         0         0         0    7.0000   -0.0000
         0         0         0         0    7.0000

u2'*u2

ans =

    1.0000    0.0000    0.0000   -0.0000   -0.0000
    0.0000    1.0000   -0.0000    0.0000    0.0000
    0.0000   -0.0000    1.0000    0.0000    0.0000
   -0.0000    0.0000    0.0000    1.0000   -0.0000
   -0.0000    0.0000    0.0000   -0.0000    1.0000

norm(u2'*u2-eye(n))

ans =

   1.3889e-15

diary off