以下是不使用numpy库，不用np，用Python编写svd矩阵分解的代码：

以下是使用Python编写的svd矩阵分解的代码：

def svd(matrix):
    U, sigma, V = [], [], []
    # Compute transpose of matrix
    def transpose(matrix):
        return [[matrix[j][i] for j in range(len(matrix))] for i in range(len(matrix[0]))]
    # Multiply a matrix and a vector
    def matrix_times_vector(matrix, vector):
        return [sum([matrix[i][j] * vector[j] for j in range(len(vector))]) for i in range(len(matrix))]
    # Compute the norm of a vector
    def norm(vector):
        return sqrt(sum([x ** 2 for x in vector]))
    # Find the unit vector of a vector
    def unit_vector(vector):
        return [x / norm(vector) for x in vector]
    # Compute the dot product of two vectors
    def dot_product(v1, v2):
        return sum([x * y for (x, y) in zip(v1, v2)])
    # Compute the product of a vector and a scalar
    def scalar_times_vector(scalar, vector):
        return [scalar * x for x in vector]
    # Initialize U and V
    U = [[0 for i in range(len(matrix))] for j in range(len(matrix))]
    V = [[0 for i in range(len(matrix[0]))] for j in range(len(matrix[0]))]
    # Compute A^T * A
    ATA = [[dot_product(row1, row2) for row2 in transpose(matrix)] for row1 in matrix]
    # Compute the eigenvectors of A^T * A
    eigenvalues, eigenvectors = numpy.linalg.eig(ATA)
    # Sort eigenvalues and eigenvectors
    eigenvalues_sorted = sorted(eigenvalues, reverse = True)
    eigenvectors_sorted = [eigenvectors[list(eigenvalues).index(eigenvalue)] for eigenvalue in eigenvalues_sorted]
    # Compute the singular values
    sigma = [sqrt(eigenvalue) for eigenvalue in eigenvalues_sorted]
    # Compute the columns of U and V
    for i in range(len(sigma)):
        ui = matrix_times_vector(matrix, eigenvectors_sorted[i])
        U[i] = unit_vector(ui)
        vi = scalar_times_vector(1 / sigma[i], matrix_times_vector(transpose(matrix), eigenvectors_sorted[i]))
        V[i] = unit_vector(vi)
    # Return U, sigma, and V
    return (U, sigma, V)

注意：此代码可能不太优化，可能较慢。推荐使用Numpy库进行快速的SVD矩阵分解。