mxnet.np.linalg.eigvals¶
-
eigvals
(a)¶ Compute the eigenvalues of a general matrix.
Main difference between eigvals and eig: the eigenvectors aren’t returned.
- Parameters
a ((.., M, M) ndarray) – A real-valued matrix whose eigenvalues will be computed.
- Returns
w – The eigenvalues, each repeated according to its multiplicity. They are not necessarily ordered.
- Return type
(.., M,) ndarray
- Raises
MXNetError – If the eigenvalue computation does not converge.
See also
eig()
eigenvalues and right eigenvectors of general arrays
eigh()
eigenvalues and eigenvectors of a real symmetric array.
eigvalsh()
eigenvalues of a real symmetric.
()
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. This function differs from the original numpy.linalg.eigvals in the following way(s): * Does not support complex input and output.
Examples
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 asA
:>>> 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 byQ.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