linalg.eigvalsh
Description
Compute the eigenvalues of a complex Hermitian or real symmetric matrix.
Main difference from eigh: The eigenvectors are not computed.
Mandatory Input Parameters
Parameter |
Type |
Description |
|---|---|---|
a |
(…, M, M) array |
Hermitian or real symmetric matrices |
Optional Input Parameters
Parameter |
Type |
Default Value |
Description |
|---|---|---|---|
UPLO |
{'L', 'U'}, |
'L' |
Specifies whether the calculation is done with the lower triangular part of a ('L') or the upper triangular part ('U'). Irrespective of this value, only the real parts of the diagonal will be considered in the calculation to preserve the notion of a Hermitian matrix. It therefore follows that the imaginary part of the diagonal will always be treated as zero. |
Return Value
Parameter |
Type |
Description |
|---|---|---|
w |
(…, M) ndarray |
The eigenvalues in ascending order, each repeated according to its multiplicity. |
Examples
>>> import numpy as np
>>> a = np.array([[1, -2j], [2j, 5]])
>>> np.linalg.eigvalsh(a)
array([0.17157288, 5.82842712])
>>>
>>> a = np.array([[5+2j, 9-2j], [0+2j, 2-1j]])
>>> a
array([[5.+2.j, 9.-2.j],
[0.+2.j, 2.-1.j]])
>>> b = np.array([[5.+0.j, 0.-2.j], [0.+2.j, 2.-0.j]])
>>> b
array([[5.+0.j, 0.-2.j],
[0.+2.j, 2.+0.j]])
>>>
>>> wa = np.linalg.eigvalsh(a)
>>> wa
array([1., 6.])
>>> wb = np.linalg.eigvalsh(b)
>>> wb
array([1., 6.])
>>> wb = np.linalg.eigvals(b)
>>> wb
array([6.+0.j, 1.+0.j])
>>>
Parent topic: Linear Algebra Functions