#模 范数
def Norm(x,v):
    if len(x[0]) == 1:
        if v == 1:
            return sum([abs(i[0]) for i in x])
        elif v == 2:
            return (sum([i[0]**2 for i in x]))**0.5
        elif v == float("inf"):
            return max([abs(i[0]) for i in x])
    else:
        if v == 1:
            return max([sum([abs(x[i][j]) for i in range(len(x))]) for j in range(len(x[0]))])
        elif v == float("inf"):
            return max([sum([abs(i) for i in x[j]]) for j in range(len(x))])
    return None
# 计算矩阵的点积
def Dot(A,B):
    if len(A[0]) != len(B):
        return None
    return [[sum([A[i][j] * B[j][k] for j in range(len(A[0]))]) for k in range(len(B[0]))] for i in range(len(A))]
        
#改成题干的矩阵##########################
if __name__ == "__main__":
    A = [[1, 3], [-2, 4]]      # 注意储存形式
    x = [[1], [-1]]            # 注意储存形式，单独一列的相量，每个数字都要中括号

    print("Norm of x with v=1:", Norm(x, 1))
    print("Norm of x with v=inf:", Norm(x, float("inf")))     # 1 1范数；2 2范数；float('inf') 无穷范数
    print("Norm of x with v=2:", Norm(x, 2))
    print("Dot product of A and x:", Dot(A, x))
    print("Norm of Ax with v=2:", Norm(Dot(A, x), 2))
    print("Norm of A with v=inf:", Norm(A, float("inf")))
    print("Norm of A with v=1:", Norm(A, 1))