`numpy.linalg:eigvals`

source: build-install/usr/lib/python3.14/site-packages/numpy/linalg/_linalg.py :1170

Signature

def eigvals ( a )

Summary

Compute the eigenvalues of a general matrix.

Extended Summary

Main difference between eigvals and eig: the eigenvectors aren't returned.

Parameters

a : (..., M, M) array_like: A complex- or real-valued matrix whose eigenvalues will be computed.

Returns

w : (..., M,) ndarray: The eigenvalues, each repeated according to its multiplicity. They are not necessarily ordered, nor are they necessarily real for real matrices.

Raises

: LinAlgError: If the eigenvalue computation does not converge.

Notes

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.

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 as ``A``:

import numpy as np
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, :])

✗

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)
A = np.dot(Q, D)
A = np.dot(A, Q.T)

✓

LA.eigvals(A)

✗

Aliases

numpy.linalg.eigvals