scipy.linalg.eig¶

scipy.linalg.eig(a, b=None, left=False, right=True, overwrite_a=False, overwrite_b=False, check_finite=True, homogeneous_eigvals=False)[source]¶

Solve an ordinary or generalized eigenvalue problem of a square matrix.

Find eigenvalues w and right or left eigenvectors of a general matrix:

a   vr[:,i] = w[i]        b   vr[:,i]
a.H vl[:,i] = w[i].conj() b.H vl[:,i]

where .H is the Hermitian conjugation.

Parameters:

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. Default is None, identity matrix is assumed. left : bool, optional Whether to calculate and return left eigenvectors. Default is False. right : bool, optional Whether to calculate and return right eigenvectors. Default is True. overwrite_a : bool, optional Whether to overwrite a; may improve performance. Default is False. overwrite_b : bool, optional Whether to overwrite b; may improve performance. Default is False. 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. The shape is (M,) unless `homogeneous_eigvals=True`. vl : (M, M) double or complex ndarray The normalized left eigenvector corresponding to the eigenvalue `w[i]` is the column vl[:,i]. Only returned if `left=True`. vr : (M, M) double or complex ndarray The normalized right eigenvector corresponding to the eigenvalue `w[i]` is the column `vr[:,i]`. Only returned if `right=True`.
Raises:	LinAlgError If eigenvalue computation does not converge.

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. Default is None, identity matrix is assumed.

left : bool, optional

Whether to calculate and return left eigenvectors. Default is False.

right : bool, optional

Whether to calculate and return right eigenvectors. Default is True.

overwrite_a : bool, optional

Whether to overwrite a; may improve performance. Default is False.

overwrite_b : bool, optional

Whether to overwrite b; may improve performance. Default is False.

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. The shape is (M,) unless homogeneous_eigvals=True.

vl : (M, M) double or complex ndarray

The normalized left eigenvector corresponding to the eigenvalue w[i] is the column vl[:,i]. Only returned if left=True.

vr : (M, M) double or complex ndarray

The normalized right eigenvector corresponding to the eigenvalue w[i] is the column vr[:,i]. Only returned if right=True.

Raises:

LinAlgError

If eigenvalue computation does not converge.