# numpy.linalg.eigvals

linalg.eigvals(a)

  Compute the eigenvalues of a general matrix.

  Main difference between `eigvals` and `eig`: the eigenvectors aren’t returned.

  Parameters
    a(…, M, M) array_like

      A complex- or real-valued matrix whose eigenvalues will be computed.

  Returns
    w(…, M,) ndarray

      The eigenvalues, each repeated according to its multiplicity. They are not necessarily ordered, nor are they necessarily real for real matrices.

  Raises
    LinAlgError

      If the eigenvalue computation does not converge.

  See also

  `eig`

    eigenvalues and right eigenvectors of general arrays

  `eigvalsh`

    eigenvalues of real symmetric or complex Hermitian (conjugate symmetric) arrays.

  `eigh`

    eigenvalues and eigenvectors of real symmetric or complex Hermitian (conjugate symmetric) arrays.

  `scipy.linalg.eigvals`

    Similar function in SciPy.

  Notes

  New in version 1.8.0.

  Broadcasting rules apply, see the `numpy.linalg` documentation for details.

  This is implemented using the `_geev` LAPACK routines which compute the eigenvalues and eigenvectors of general square arrays.

  Examples

  Illustration, using the fact that the eigenvalues of a diagonal matrix are its diagonal elements, that multiplying a matrix on the left by an orthogonal matrix, Q, and on the right by Q.T (the transpose of Q), preserves the eigenvalues of the “middle” matrix. In other words, if Q is orthogonal, then `Q * A * Q.T` has the same eigenvalues as `A`:

      >>> from numpy import linalg as LA
      >>> x = np.random.random()
      >>> Q = np.array([[np.cos(x), -np.sin(x)], [np.sin(x), np.cos(x)]])
      >>> LA.norm(Q[0, :]), LA.norm(Q[1, :]), np.dot(Q[0, :],Q[1, :])
      (1.0, 1.0, 0.0)

  Now multiply a diagonal matrix by `Q` on one side and by `Q.T` on the other:

      >>> D = np.diag((-1,1))
      >>> LA.eigvals(D)
      array([-1.,  1.])
      >>> A = np.dot(Q, D)
      >>> A = np.dot(A, Q.T)
      >>> LA.eigvals(A)
      array([ 1., -1.]) # random

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