如何确定两个数学向量是否相同？

def are_vectors_equal(vector1, vector2):
    # 检查维度是否相同
    if len(vector1) != len(vector2):
        return False
    
    # 逐个比较分量
    for i in range(len(vector1)):
        if vector1[i] != vector2[i]:
            return False
    
    return True

# 示例使用
vector_a = [1, 2, 3]
vector_b = [1, 2, 3]
vector_c = [1, 2, 4]

print(are_vectors_equal(vector_a, vector_b))  # 输出: True
print(are_vectors_equal(vector_a, vector_c))  # 输出: False

def are_vectors_equal_with_tolerance(vector1, vector2, tolerance=1e-9):
    if len(vector1) != len(vector2):
        return False
    
    for i in range(len(vector1)):
        if abs(vector1[i] - vector2[i]) > tolerance:
            return False
    
    return True