'orth' command -- question

[John B. Thoo]

Hi.  I'm trying to understand the command 'orth'.

Example 1
---------
octave-3.2.3:46> A = [1, 2, 2; 2, 1, 2; 2, 2, 1];

octave-3.2.3:47> [V, LAMBDA] = eig (A); P = orth (V)
P =

   0.62060  -0.53058   0.57735
   0.14920   0.80275   0.57735
  -0.76980  -0.27217   0.57735

octave-3.2.3:48> P'*A*P
ans =

  -1.0000e+00   2.7756e-17  -9.4369e-16
   1.1102e-16  -1.0000e+00   8.6042e-16
  -8.8818e-16   7.7716e-16   5.0000e+00


So, it appears that 'orth' provides an orthonormal basis of eigenvectors of  A.

Example 2
---------
octave-3.2.3:66> A = [4, 1, 0; 1, 4, 1; 0, 1, 4];
octave-3.2.3:67> [V, LAMBDA] = eig (A); P = orth (V)
P =

  -0.023793   0.865699   0.500000
  -0.588348   0.392232  -0.707107
  -0.808257  -0.310998   0.500000

octave-3.2.3:68> P'*A*P
ans =

   4.9791e+00  -6.5271e-01   2.2204e-16
  -6.5271e-01   4.4351e+00   9.9920e-16
   4.4409e-16   6.1062e-16   2.5858e+00

Now it appears that 'orth' does _not_ provide an orthonormal basis of 
eigenvectors of  A.

Why does 'orth' appear to behave differently in the two examples?

Thanks.

---John.

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"Ten thousand difficulties do not make one doubt....  A man may be annoyed that 
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