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>> v1 = [1 1 1]'

v1 =

     1
     1
     1

>> v2 = [1 2 3]'

v2 =

     1
     2
     3

>> v3 = [1-i -i 0]'

v3 =

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

>> u1 = v1/norm(v1)

u1 =

    0.5774
    0.5774
    0.5774

>> w2 = v2-(u1'*v2)*u1

w2 =

   -1.0000
   -0.0000
    1.0000

>> u2 = w2/norm(w2)

u2 =

   -0.7071
   -0.0000
    0.7071

>> w3 = v3 - (u1'*v3)*u1 - (u2'*v3)*u2

w3 =

   0.1667 - 0.1667i
  -0.3333 + 0.3333i
   0.1667 - 0.1667i

>> v3 = w3/norm(w3)

v3 =

   0.2887 - 0.2887i
  -0.5774 + 0.5774i
   0.2887 - 0.2887i