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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]

  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]])