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

>>> 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]])