np.linalg.inv raises LinAlgError for a singular matrix even after adding a small epsilon to the diagonal
I'm stuck on something that should probably be simple. This might be a silly question, but I'm working with an scenario when trying to compute the inverse of a matrix using `np.linalg.inv`. I have a matrix that is nearly singular and even after attempting to stabilize it by adding a small epsilon value to its diagonal, I'm still receiving the behavior `LinAlgError: Singular matrix`. Here's what I've tried: ```python import numpy as np # Create a nearly singular matrix A = np.array([[1, 1], [1, 1 + 1e-10]]) # Attempt to stabilize the matrix by adding a small epsilon epsilon = 1e-5 A_stable = A + np.eye(A.shape[0]) * epsilon # Trying to compute the inverse try: A_inv = np.linalg.inv(A_stable) print("Inverse computed successfully:", A_inv) except np.linalg.LinAlgError as e: print("behavior:", e) ``` Despite adding a small value to the diagonal, the matrix is still being treated as singular. I would expect this approach to work, as slightly perturbing the diagonal should prevent singularity. Are there any best practices or alternative methods to handle nearly singular matrices in NumPy, or is there something I might be missing in this approach? I'm using NumPy version 1.23.0. I'm working on a API that needs to handle this. I'm working on a service that needs to handle this. Has anyone else encountered this? For context: I'm using Python on CentOS. I'm coming from a different tech stack and learning Python.