import numpy as np

def LRZerlegungVektorisiert(A):
    n = A.shape[0]
    L = np.eye(n)
    R = A.astype('float').copy()
    for kk in range(n - 1):
        L[kk+1:, kk] = R[kk+1:, kk] / R[kk, kk]
        R[kk+1:, :]  = R[kk+1:, :] - L[kk+1:, [ kk ]] * R[[ kk ], :]
    return L, R