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 - wis 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]])