Tensorflow Eigenvalues / EigenVector (tf.linalg.eigh)

Question

I'm attempting to verify a simple eigenvalue / eigenvector problem using TensorFlow.

Import tensorflow:

import tensorflow as tf # version 2.6.0

For example, take a simple Matrix

ex1 = tf.convert_to_tensor([[0,1],[-2,-3]],dtype=tf.float32)
print(ex1)

Output:

tf.Tensor(
[[ 0.  1.]
 [-2. -3.]], shape=(2, 2), dtype=float32)

I then calculate the eigenvalues and eigenvectors using tf.linalg.eigh:

eigVals, eigVects = tf.linalg.eigh(ex1)
print(tf.linalg.diag(eigVals),eigVects)

Output:

tf.Tensor(
[[-4.         0.       ]
 [ 0.         1.0000001]], shape=(2, 2), dtype=float32) tf.Tensor(
[[ 0.4472136  0.8944272]
 [ 0.8944272 -0.4472136]], shape=(2, 2), dtype=float32)

Now, since the eigenvalues and eigenvectors for A are defined as Av = Lv, I can calculate Av and Lv and should get matching answers (within rounding error):

Calculating Av:

tf.matmul(ex1,eigVects)

Output:

<tf.Tensor: shape=(2, 2), dtype=float32, numpy=
array([[ 0.8944272 , -0.4472136 ],
       [-3.5777087 , -0.44721365]], dtype=float32)>

and calculating Lv:

tf.matmul(tf.linalg.diag(eigVals),eigVects)

Output:

<tf.Tensor: shape=(2, 2), dtype=float32, numpy=
array([[-1.7888544 , -3.5777087 ],
       [ 0.8944273 , -0.44721365]], dtype=float32)>

Why don't these match?

Answer 1

According to the documentation of eigh:

Computes the eigen decomposition of a batch of self-adjoint matrices.