How to compute the eigenvalues and eigenvectors of a square matrix in PyTorch?

In this article, we are going to discuss how to compute the eigenvalues and eigenvectors of a square matrix in PyTorch.

Compute the eigenvalues and eigenvectors of a square matrix in PyTorch

torch.linalg.eig() method computes the eigenvalue decomposition of a square matrix or a batch of matrices. The decomposition exists if the input matrix is diagonalizable. This method also supports the input of float, double, cfloat, and cdouble data types. It will return a named tuple (eigenvalues, eigenvectors). The eigenvalues and eigenvectors are always complex-valued and the eigenvectors are given by columns of eigenvectors. Below is the syntax of torch.linalg.eig() method.

Syntax: torch.linalg.eig(mat)

Parameter:

• mat (Tensor): square matrix or a batch of matrices.

Return: It will return a named tuple (eigenvalues, eigenvectors).

Example 1:

In this example, we see how to compute the eigenvalues and eigenvectors of a square matrix.

Python3

# import the required library
import torch

# define a 3x3 square matrix
mat = torch.tensor([[-0.3371, -0.2975, 1.8739],
                    [1.4078, 1.6856, 0.3799],
                    [1.9002, -0.4428, 1.5552]])

# print the above created matrix
print("\n Matrix: \n", mat)

# compute the eigenvalues and eigenvectors
eigenvalues, eigenvectors = torch.linalg.eig(mat)

# print output
print("\n Eigenvalues: \n", eigenvalues)
print("\n Eigenvectors: \n", eigenvectors)

Output:

EigenValues and EigenVectors

Example 2:

In this example, we see how to compute the eigenvalues and eigenvectors of a batch of matrices.

Python3

# import the required library
import torch

# define a batch of matrices
mat = torch.tensor([[[-0.1345, -0.7437, 1.2377],
                     [0.9337, 1.6473, 0.4346],
                     [-1.6345, 0.9344, -0.2456]],
                    [[1.3343, -1.3456, 0.7373],
                     [1.4334, 0.2473, 1.1333],
                     [-1.5341, 1.5348, -1.4567]]])

# print the above batch of matrices
print("\n Matrix: \n", mat)

# compute the eigenvalues and eigenvectors
eigenvalues, eigenvectors = torch.linalg.eig(mat)

# print output
print("\n Eigenvalues: \n", eigenvalues)
print("\n Eigenvectors: \n", eigenvectors)

Output:

EigenValues and EigenVectors