scipy.linalg.eig¶
- scipy.linalg.eig(a, b=None, left=False, right=True, overwrite_a=False, overwrite_b=False, check_finite=True)[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: 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 : boolean, 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.
Returns: w : (M,) double or complex ndarray
The eigenvalues, each repeated according to its multiplicity.
vl : (M, M) double or complex ndarray
The normalized left eigenvector corresponding to the eigenvalue w[i] is the column v[:,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.
See also
- eigh
- Eigenvalues and right eigenvectors for symmetric/Hermitian arrays.