How SVD works in matrix factorization

Question

I want to know about the ways of factorizing a matrix using SVD (Singular Value Decomposition). I found several articles, I have gone through many of them but i am not getting a clear idea about factorizing a matrix using SVD. What i found is , SVD finds M = UΣV^T . After performing calculations according to this article, I can find U , Σ , V . Now i want to know, is the U & V are my factorized matrices ?

https://towardsdatascience.com/recommendation-system-matrix-factorization-svd-explained-c9a50d93e488

And how can i implement this in python ?

| 1   | 2   | 3   | 5   |     
| 2   | 4   | 8   | 12  |
| 3   | 6   | 7   | 13  |

lets assume above matrix, I want to have two factorized matrices like below

First factorized matrix

| 1   | 2   |    
| 2   | 4   |
| 3   | 6   |

Second factorized matrix

| 1   | 2   | 0   | 2   |     
| 0   | 0   | 1   | 1   |

Answer 1

I think this is the simplest implementation of SVD in Python:

import numpy as np

# Define a matrix A
A = np.array([[1, 2, 3, 5], [2, 4, 8, 12], [3, 6, 7, 13]])

# Use SVD to decompose A into its singular values and singular vectors
U, S, V = np.linalg.svd(A)

# Print the results
print("U:", U)
print("S:", S)
print("V:", V)