eig

paddle.linalg. eig ( x: Tensor, name: str | None = None ) → tuple[Tensor, Tensor] [source]

Performs the eigenvalue decomposition of a square matrix or a batch of square matrices.

Note

If the matrix is a Hermitian or a real symmetric matrix, please use eigh instead, which is much faster.
If only eigenvalues is needed, please use eigvals instead.
If the matrix is of any shape, please use svd.
This API is only supported on CPU device.
The output datatype is always complex for both real and complex input.

Parameters

x (Tensor) – A tensor with shape math:[*, N, N], The data type of the x should be one of float32, float64, complex64 or complex128.
name (str|None, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to api_guide_Name.

Returns

A tensor with shape math:[*, N] refers to the eigen values. Eigenvectors(Tensor): A tensor with shape math:[*, N, N] refers to the eigen vectors.

Return type

Eigenvalues(Tensor)

Examples

           >>> import paddle

>>> x = paddle.to_tensor(
...     [
...         [1.6707249, 7.2249975, 6.5045543],
...         [9.956216, 8.749598, 6.066444],
...         [4.4251957, 1.7983172, 0.370647],
...     ]
... )
>>> w, v = paddle.linalg.eig(x)
>>> print(v)
Tensor(shape=[3, 3], dtype=complex64, place=Place(cpu), stop_gradient=True,
[[ (0.50613654+0.00000000j),  (0.79717612+0.00000000j),
   (0.18518065+0.00000000j)],
 [ (0.83082366+0.00000000j), (-0.34638131+0.00000000j),
  (-0.68370056+0.00000000j)],
 [ (0.23142573+0.00000000j), (-0.49449989+0.00000000j),
   (0.70587653+0.00000000j)]])

>>> print(w)
Tensor(shape=[3], dtype=complex64, place=Place(cpu), stop_gradient=True,
[(16.50470734+0.00000000j), (-5.50348139+0.00000000j),
 (-0.21026139+0.00000000j)])

          