eigvals(a)
Main difference between eigvals
and eig
: the eigenvectors aren't returned.
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.
A complex- or real-valued matrix whose eigenvalues will be computed.
If the eigenvalue computation does not converge.
The eigenvalues, each repeated according to its multiplicity. They are not necessarily ordered, nor are they necessarily real for real matrices.
Compute the eigenvalues of a general matrix.
eig
eigenvalues and right eigenvectors of general arrays
eigh
eigenvalues and eigenvectors of real symmetric or complex Hermitian (conjugate symmetric) arrays.
eigvalsh
eigenvalues of real symmetric or complex Hermitian (conjugate symmetric) arrays.
scipy.linalg.eigvals
Similar function in SciPy.
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, :None:None:`Q`, and on the right by :None:None:`Q.T` (the transpose of :None:None:`Q`), preserves the eigenvalues of the "middle" matrix. In other words, if :None:None:`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)See :
... A = np.dot(A, Q.T)
... LA.eigvals(A) array([ 1., -1.]) # random
The following pages refer to to this document either explicitly or contain code examples using this.
numpy.linalg.eigvals
numpy.linalg.eigvalsh
numpy.linalg.eigh
numpy.linalg.eig
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