# How to Solve the Generalised Eigenvalue Problem in Python?

The Generalized Eigenvalue Problem is a mathematical problem that asks you to find the eigenvalues and eigenvectors of a pair of matrices. Here is an example of how to solve this problem in Python using the NumPy library:

``````import numpy as np

# create two matrices A and B
A = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
B = np.array([[9, 8, 7], [6, 5, 4], [3, 2, 1]])

# compute the eigenvalues and eigenvectors of the generalized eigenvalue problem
eigenvalues, eigenvectors = np.linalg.eig(A, B)

# print the results
print("Eigenvalues:\n", eigenvalues)
print("Eigenvectors:\n", eigenvectors)``````

In this solution, we first create two matrices `A` and `B` as NumPy arrays. These matrices represent the coefficients of a pair of linear equations.

We then use the `np.linalg.eig` function to compute the eigenvalues and eigenvectors of the generalized eigenvalue problem. The function takes two input matrices and returns two output arrays: `eigenvalues` and `eigenvectors`.

The `eigenvalues` array contains the eigenvalues of the problem, while the `eigenvectors` array contains the corresponding eigenvectors. Each column of `eigenvectors` represents an eigenvector of the problem.

Finally, we print out the results of the computation using the `print` function.

To use this code, simply replace the matrices `A` and `B` with your own matrices and run the script. The output will be the eigenvalues and eigenvectors of the generalized eigenvalue problem.