Compute Eigenvalues and Eigenvectors of a Square Matrix in PyTorch

torch.linalg.eig() computes the Eigen value decomposition of a square matrix or a batch of square matrices. It accepts matrix and batch of matrices of float, double, cfloat and cdouble data types. It returns a named tuple (eigenvalues, eigenvectors). The eigenvalues and eigenvectors are always complex valued. The eigenvectors are given by columns of eigenvectors.

Syntax

(eigenvalues, eigenvectors) = torch.linalg.eig(A)

Where A is a square matrix or a batch of square matrices. It returns a named tuple (eigenvalues, eigenvectors).

Steps

• Import the required library. In all the following examples, the required Python library is torch. Make sure you have already installed it.

import torch

• Create a square matrix or batch of square matrices. Here we define a square matrix (a 2D torch tensor) of size [3, 3].

A = torch.randn(3,3)

• Compute Eigen value decomposition of square matrix or batch of square matrices using torch.linalg.eig(A). Here A is square matrix.

eigenvalues, eigenvectors = torch.linalg.eig(A)

• Display eigenvalues and eigenvectors.

print("Eigen Values:
", eigenvalues)
print("Eigen Vectors:
", eigenvectors)

Example 1

In this program, we compute the eigenvalues and eigenvectors of a square matrix.

# import required library
import torch

# create a 3x3 square matrix
A = torch.randn(3,3)

# print the above created matrix
print("Matrix:
", A)

# compute the Eigen values and vectors of the matrix
eigenvalues, eigenvectors = torch.linalg.eig(A)

print("Eigen Values:
", eigenvalues)
print("Eigen Vectors:
", eigenvectors)

Output

It will produce the following output −

Matrix:
   tensor([[-0.7412, 0.6472, -0.4741],
      [ 1.8981, 0.2936, -1.9471],
      [-0.1449, 0.0327, -0.8543]])
Eigen Values:
   tensor([ 1.0190+0.j, -1.3846+0.j, -0.9364+0.j])
Eigen Vectors:
   tensor([[-0.3476+0.j, -0.7716+0.j, 0.5184+0.j],
      [-0.9376+0.j, 0.5862+0.j, 0.3982+0.j],
      [ 0.0105+0.j, -0.2469+0.j, 0.7568+0.j]])

Example 2

In this program, we compute eigenvalues and eigenvectors of a square complex matrix.

# import required library
import torch

# create a 2x2 square complex matrix
A = torch.randn(2,2, dtype = torch.cfloat )

# print the above created matrix
print("Matrix:
", A)

# computet the eigen values and vectors of the matrix
eigenvalues, eigenvectors = torch.linalg.eig(A)

print("Eigen Values:
", eigenvalues)
print("Eigen Vectors:
", eigenvectors)

Output

It will produce the following output −

Matrix:
   tensor([[-0.1068-0.0045j, 0.7061-0.5698j],
      [-0.2521-1.1166j, 0.6921+1.4637j]])
Eigen Values:
   tensor([0.3194-0.3633j, 0.2659+1.8225j])
Eigen Vectors:
   tensor([[ 0.8522+0.0000j, -0.2012-0.3886j],
      [ 0.5231-0.0109j, 0.8992+0.0000j]])