### Navigation

- index
- modules |
- next |
- previous |
- NumPy v1.3 Manual (DRAFT) »
- NumPy Reference »
- Routines »
- Linear algebra (`numpy.linalg`) »

# numpy.linalg.eigh

`numpy.linalg.``eigh`(a, UPLO='L')

  Eigenvalues and eigenvectors of a Hermitian or real symmetric matrix.

  Parameters: | a : array_like, shape (M, M) A complex Hermitian or symmetric real matrix. UPLO : {‘L’, ‘U’}, optional Specifies whether the calculation is done with data from the lower triangular part of a (‘L’, default) or the upper triangular part (‘U’).
  Returns: | w : ndarray, shape (M,) The eigenvalues. The eigenvalues are not necessarily ordered. v : ndarray, shape (M, M) The normalized eigenvector corresponding to the eigenvalue w[i] is the column v[:,i].
  Raises: | LinAlgError : If the eigenvalue computation does not converge.

  See also

  `eigvalsh`
    eigenvalues of symmetric or Hemitiean arrays.
  `eig`
    eigenvalues and right eigenvectors for non-symmetric arrays
  `eigvals`
    eigenvalues of non-symmetric array.

  Notes

  A simple interface to the LAPACK routines dsyevd and zheevd that compute the eigenvalues and eigenvectors of real symmetric and complex Hermitian arrays respectively.

  The number w is an eigenvalue of a if there exists a vector v satisfying the equation dot(a,v) = w*v. Alternately, if w is a root of the characteristic equation det(a - w[i]*I) = 0, where det is the determinant and I is the identity matrix. The eigenvalues of real symmetric or complex Hermitean matrices are always real. The array v of eigenvectors is unitary and a, w, and v satisfy the equation dot(a,v[i]) = w[i]*v[:,i].

### Navigation

- index
- modules |
- next |
- previous |
- NumPy v1.3 Manual (DRAFT) »
- NumPy Reference »
- Routines »
- Linear algebra (`numpy.linalg`) »