The Cholesky decomposition is another way of solving systems of linear equations. It can be significantly faster and uses a lot of less memory than the LU decomposition by exploiting the property of symmetric matrices. However, it is required that the matrix being decomposed be Hermitian (or real-valued symmetric and thus square) and positive definite. This means that when the matrix A is decomposed as , L is a lower triangular matrix with real and positive numbers on the diagonals, and is the conjugate transpose of L.

Let's consider another example of a system of linear equations where matrix A is both Hermitian and positive definite. Again, the equation is in the form of , where A and B take the following values:

Let's represent these matrices as the NumPy arrays:

""" Cholesky decomposition with NumPy """
import numpy as np

A = np.array([[10., -1., 2., 0.],
              [-1., 11., -1., 3.],
              [2., -1., 10., -1.],
              [0.0, 3., -1., 8.]]...