A fast LU decomposition algorithm, along with computing the determinant

det.py

def matrixMul(A, B):
    TB = list(zip(*B))
    return [[sum(ea*eb for ea,eb in zip(a,b)) for b in TB] for a in A]

def pivotize(m):
    """Creates the pivoting matrix for m."""
    n = len(m)
    ID = [[float(i == j) for i in range(n)] for j in range(n)]
    r = 0
    for j in range(n):
        row = max(range(j, n), key=lambda i: abs(m[i][j]))
        if j != row:
            ID[j], ID[row] = ID[row], ID[j]
            r += 1
    return ID, r

def lu(A):
    """Decomposes a nxn matrix A by PA=LU and returns L, U and P."""
    n = len(A)
    L = [[0.0] * n for i in range(n)]
    U = [[0.0] * n for i in range(n)]
    P, r = pivotize(A)
    A2 = matrixMul(P, A)
    for j in range(n):
        L[j][j] = 1.0
        for i in range(j+1):
            s1 = sum(U[k][j] * L[i][k] for k in range(i))
            U[i][j] = A2[i][j] - s1
        for i in range(j, n):
            s2 = sum(U[k][j] * L[i][k] for k in range(j))
            L[i][j] = (A2[i][j] - s2) / U[j][j]
    return (L, U, P, r)
def trace(m):
    n = len(m)
    r = 1
    for i in range(n):
        if len(m[i]) <= i:
            break
        r *= m[i][i]
    return r
def det(m):
    l, u, p, r = lu(m)
    return (-1)**r * trace(l) * trace(u)
mat = [[1, 3, 5], [2, 4, 7], [1, 1, 0]]
print(det(mat))

http://rosettacode.org/wiki/LU_decomposition#Python