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Compute the eigenvalues of a complex Hermitian or real symmetric matrix in Python
To compute the eigenvalues of a complex Hermitian or real symmetric matrix, use the numpy.eigvalsh() method. The method returns the eigenvalues in ascending order, each repeated according to its multiplicity.
The 1st parameter, a is a complex- or real-valued matrix whose eigenvalues are to be computed. The 2nd parameter, UPLO specifies whether the calculation is done with the lower triangular part of a (‘L’, default) or the upper triangular part (‘U’). Irrespective of this value only the real parts of the diagonal will be considered in the computation to preserve the notion of a Hermitian matrix. It therefore follows that the imaginary part of the diagonal will always be treated as zero.
Steps
At first, import the required libraries -
import numpy as np from numpy import linalg as LA
Creating a 2D numpy array using the numpy.array() method −
arr = np.array([[5+2j, 9-2j], [0+2j, 2-1j]])
Display the array −
print("Our Array...\n",arr)Check the Dimensions −
print("\nDimensions of our Array...\n",arr.ndim)
Get the Datatype −
print("\nDatatype of our Array object...\n",arr.dtype)Get the Shape −
print("\nShape of our Array object...\n",arr.shape)
To compute the eigenvalues of a complex Hermitian or real symmetric matrix, use the numpy.eigvalsh() method −
print("\nResult...\n",LA.eigvalsh(arr))Example
from numpy import linalg as LA
import numpy as np
# Creating a 2D numpy array using the numpy.array() method
arr = np.array([[5+2j, 9-2j], [0+2j, 2-1j]])
# Display the array
print("Our Array...\n",arr)
# Check the Dimensions
print("\nDimensions of our Array...\n",arr.ndim)
# Get the Datatype
print("\nDatatype of our Array object...\n",arr.dtype)
# Get the Shape
print("\nShape of our Array object...\n",arr.shape)
# To compute the eigenvalues of a complex Hermitian or real symmetric matrix, use the numpy.eigvalsh() method
print("\nResult...\n",LA.eigvalsh(arr))Output
Our Array... [[5.+2.j 9.-2.j] [0.+2.j 2.-1.j]] Dimensions of our Array... 2 Datatype of our Array object... complex128 Shape of our Array object... (2, 2) Result... [1. 6.]
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