# numpy.linalg.eigvals¶

`numpy.linalg.``eigvals`(a)[source]

Compute the eigenvalues of a general matrix.

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. w : (…, M,) ndarray The eigenvalues, each repeated according to its multiplicity. They are not necessarily ordered, nor are they necessarily real for real matrices. LinAlgError If the eigenvalue computation does not converge.

`eig`
eigenvalues and right eigenvectors of general arrays
`eigvalsh`
eigenvalues of real symmetric or complex Hermitian (conjugate symmetric) arrays.
`eigh`
eigenvalues and eigenvectors of real symmetric or complex Hermitian (conjugate symmetric) arrays.

Notes

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.

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`:

```>>> 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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