scipy.linalg.

eigvals#

scipy.linalg.eigvals(a, b=None, overwrite_a=False, check_finite=True, homogeneous_eigvals=False)[source]#

Compute eigenvalues from an ordinary or generalized eigenvalue problem.

Find eigenvalues of a general matrix:

a   vr[:,i] = w[i]        b   vr[:,i]

The documentation is written assuming array arguments are of specified “core” shapes. However, array argument(s) of this function may have additional “batch” dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see Batched Linear Operations for details.

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

>>> import numpy as np
>>> 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]])