numpy.linalg.eigvals(a)
[source]
Compute the eigenvalues of a general matrix.
Main difference between eigvals
and eig
: the eigenvectors aren’t returned.
Parameters: 


Returns: 

Raises: 

See also
New in version 1.8.0.
Broadcasting rules apply, see the numpy.linalg
documentation for details.
This is implemented using the _geev
LAPACK routines which compute the eigenvalues and eigenvectors of general square arrays.
Illustration, using the fact that the eigenvalues of a diagonal matrix are its diagonal elements, that multiplying a matrix on the left by an orthogonal matrix, Q
, and on the right by Q.T
(the transpose of Q
), preserves the eigenvalues of the “middle” matrix. In other words, if Q
is orthogonal, then Q * A * Q.T
has the same eigenvalues as A
:
>>> from numpy import linalg as LA >>> x = np.random.random() >>> Q = np.array([[np.cos(x), np.sin(x)], [np.sin(x), np.cos(x)]]) >>> LA.norm(Q[0, :]), LA.norm(Q[1, :]), np.dot(Q[0, :],Q[1, :]) (1.0, 1.0, 0.0)
Now multiply a diagonal matrix by Q
on one side and by Q.T
on the other:
>>> D = np.diag((1,1)) >>> LA.eigvals(D) array([1., 1.]) >>> A = np.dot(Q, D) >>> A = np.dot(A, Q.T) >>> LA.eigvals(A) array([ 1., 1.]) # random
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https://docs.scipy.org/doc/numpy1.17.0/reference/generated/numpy.linalg.eigvals.html