pytorchlinear-algebraeigenvalueeigenvector

Why don't eigenpairs calculated through torch.linalg.eig pass the eigenpair test?

Running the following code:

import torch

torch.manual_seed(47)

m = torch.rand([8, 8])

eigvals, eigvecs = torch.linalg.eig(m)

print(m.type(torch.complex64) @ eigvecs[0] - eigvals[0] * eigvecs[0])  # Should be close to →0.

Results with output:

tensor([ 2.2827+0.0995j, -0.9539-0.0442j, -1.9871-0.0204j, -0.6442-0.0372j,
        -0.8338-0.0518j,  1.2168-0.0077j,  0.4924-0.5008j,  0.9643+0.4292j])

What is going on here? How is it that the eigenpair test fails?

Solution

  • The documentation of torch.linalg.eig states that the eigenvectors will be given by the columns of the resulting tensor (eigvecs in your case), what you got with eigvecs[0] was the first row.

    Using eigvecs.T[0] or eigvecs[:, 0] will yield the expected (i.e. close to zero) result:

    print(m.type(torch.complex64) @ eigvecs.T[0] - eigvals[0] * eigvecs.T[0])
# >>> tensor([ 3.5763e-07+0.j,  5.9605e-07+0.j,  4.7684e-07+0.j,  2.3842e-07+0.j,
#              3.5763e-07+0.j,  2.3842e-07+0.j, -2.3842e-07+0.j,  1.1921e-07+0.j])