cholesky matrix decomposition is used to find the decomposition of a hermitian positivedefinite matrix a into matrix v so that v v a where v denotes the conjugate transpose of l the dimensions of the matrix a must match this method is mainly used for numeric solution of linear equations ax b example input matrix a 4 12 16 12 37 43 16 43 98 result 2 0 0 0 0 0 6 0 1 0 0 0 8 0 5 0 3 0 time complexity of this algorithm is on3 specifically about n33 param a hermitian positivedefinite matrix of type listlistfloat return matrix of type listlistfloat if a can be decomposed otherwise none param a hermitian positive definite matrix of type list list float return matrix of type list list float if a can be decomposed otherwise none
import math


def cholesky_decomposition(A):
    
    n = len(A)
    for ai in A:
        if len(ai) != n:
            return None
    V = [[0.0] * n for _ in range(n)]
    for j in range(n):
        sum_diagonal_element = 0
        for k in range(j):
            sum_diagonal_element = sum_diagonal_element + math.pow(V[j][k], 2)
        sum_diagonal_element = A[j][j] - sum_diagonal_element
        if sum_diagonal_element <= 0:
            return None
        V[j][j] = math.pow(sum_diagonal_element, 0.5)
        for i in range(j+1, n):
            sum_other_element = 0
            for k in range(j):
                sum_other_element += V[i][k]*V[j][k]
            V[i][j] = (A[i][j] - sum_other_element)/V[j][j]
    return V