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scipy.linalg.

# eigvals

scipy.linalg.eigvals(a, b=None, overwrite_a=False, check_finite=True, homogeneous_eigvals=False)

  Compute eigenvalues from an ordinary or generalized eigenvalue problem.

  Find eigenvalues of a general matrix:

      a   vr[:,i] = w[i]        b   vr[:,i]

  The documentation is written assuming array arguments are of specified “core” shapes. However, array argument(s) of this function may have additional “batch” dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see Batched Linear Operations for details.

  Parameters:
    a(M, M) array_like

      A complex or real matrix whose eigenvalues and eigenvectors will be computed.

    b(M, M) array_like, optional

      Right-hand side matrix in a generalized eigenvalue problem. If omitted, identity matrix is assumed.

    overwrite_a bool, optional

      Whether to overwrite data in a (may improve performance)

    check_finite bool, optional

      Whether to check that the input matrices contain only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs.

    homogeneous_eigvals bool, optional

      If True, return the eigenvalues in homogeneous coordinates. In this case `w` is a (2, M) array so that:

          w[1,i] a vr[:,i] = w[0,i] b vr[:,i]

      Default is False.

  Returns:
    w(M,) or (2, M) double or complex ndarray

      The eigenvalues, each repeated according to its multiplicity but not in any specific order. The shape is (M,) unless `homogeneous_eigvals=True`.

  Raises:
    LinAlgError

      If eigenvalue computation does not converge

  See also

  `eig`

    eigenvalues and right eigenvectors of general arrays.

  `eigvalsh`

    eigenvalues of symmetric or Hermitian arrays

  `eigvals_banded`

    eigenvalues for symmetric/Hermitian band matrices

  `eigvalsh_tridiagonal`

    eigenvalues of symmetric/Hermitian tridiagonal matrices

  Examples

      >>> import numpy as np
      >>> from scipy import linalg
      >>> a = np.array([[0., -1.], [1., 0.]])
      >>> linalg.eigvals(a)
      array([0.+1.j, 0.-1.j])

      >>> b = np.array([[0., 1.], [1., 1.]])
      >>> linalg.eigvals(a, b)
      array([ 1.+0.j, -1.+0.j])

      >>> a = np.array([[3., 0., 0.], [0., 8., 0.], [0., 0., 7.]])
      >>> linalg.eigvals(a, homogeneous_eigvals=True)
      array([[3.+0.j, 8.+0.j, 7.+0.j],
             [1.+0.j, 1.+0.j, 1.+0.j]])