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_abool, optional

Whether to overwrite data in a (may improve performance)

check_finitebool, 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_eigvalsbool, 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]])