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# 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

  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`:

      >>> import numpy as np
      >>> 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