首先创建矩阵基本操作，首先构造下图中的矩阵，特别注意：一维矩阵的建立格式。
from sympy import *import math import numpy as npa = Matrix([[3,5],[-1,1],[0,5]])print(a)b = Matrix([1,2,3])#三行一列print(b.shape)c = Matrix([[1,2,3]])print(c.shape)x = Matrix([[1,3,4],[4,2,1]])y = Matrix([0,1,1])print(x*y)#两行一列运行结果
Matrix([[3, 5], [-1, 1], [0, 5]])(3, 1)(1, 3)Matrix([[7], [3]]) 列和行的操作列和行的操作，M.row(0)将的到第一行,M.col(-1)会得到最后一列
M = Matrix([[1,3,2],[5,6,3]])print(M.shape)#打印矩阵的维度"""列和行的操作，M.row(0)将的到第一行,M.col(-1)会得到最后一列"""print("打印第一行")print(M.row(0))print("打印最后一列")print(M.col(-1)) (2, 3)打印第一行Matrix([[1, 3, 2]])打印最后一列Matrix([[2], [3]]) 删除和插入数据操作 M = Matrix([[1,3,2],[5,6,3]])print(M.shape)#打印矩阵的维度"""删除矩阵的行或列，用 row_del和col_del"""M.col_del(0)print(M)M.row_del(1)print(M)print("给矩阵添加行或列，用 row_del和col_del")print(M)M = M.row_insert(1,Matrix([[0,4]]))#添加行print("在第二行添加数据")print(M)M = M.col_insert(0,Matrix([1,-2]))print("在第一列添加数据")print(M) (2, 3)Matrix([[3, 2], [6, 3]])Matrix([[3, 2]])给矩阵添加行或列，用 row_del和col_delMatrix([[3, 2]])在第二行添加数据Matrix([[3, 2], [0, 4]])在第一列添加数据Matrix([[1, 3, 2], [-2, 0, 4]]) 基本数学运算 M = Matrix([[1,3],[5,3]])N = Matrix([[4,3],[8,1]])print("矩阵相加")print(M+N)print("矩阵相乘")print(radyz)print("矩阵的平方")print(M**2)print("矩阵乘以一个数")print(M*3)print("求矩阵的逆")print(M**-1)print("矩阵的转置")print(M.T) 矩阵相加Matrix([[5, 6], [13, 4]])矩阵相乘Matrix([[28, 6], [44, 18]])矩阵的平方Matrix([[16, 12], [20, 24]])矩阵乘以一个数Matrix([[3, 9], [15, 9]])求矩阵的逆Matrix([[-1/4, 1/4], [5/12, -1/12]])矩阵的转置Matrix([[1, 5], [3, 3]]) 矩阵的高级操作 M = Matrix([[1,3,4],[5,0,3],[3,5,7]])print(M)print("计算矩阵的行列式")print(M.det())print("化简矩阵,返回两个元素，第一个是矩阵，第二个是元组")print(M.rref()) Matrix([[1, 3, 4], [5, 0, 3], [3, 5, 7]])计算矩阵的行列式7化简矩阵(Matrix([[1, 0, 0],[0, 1, 0],[0, 0, 1]]), [0, 1, 2]) 特征值、特征向量和对角化 特征值 M = Matrix([[3,-2,4,-2],[5,3,-3,-2],[5,-2,2,-2],[5,-2,-3,3]])print(M)print("计算矩阵的特征值")print(M.eigenvals())Matrix([[3, -2, 4, -2], [5, 3, -3, -2], [5, -2, 2, -2], [5, -2, -3, 3]])
计算矩阵的特征值
{3: 1, -2: 1, 5: 2}，M的特征值为-2,3,5，特征值-2,3具有代数多重性1，特征值5具有代数多重性2.
计算矩阵的特征向量
[(-2, 1, [Matrix([[0],[1],[1],[1]])]),
(3, 1, [Matrix([[1],[1],[1],[1]])]),
(5, 2, [Matrix([[1],[1],[1],[0]]), Matrix([[ 0],[-1],[ 0],[ 1]])])]，
对角化 M = Matrix([[3,-2,4,-2],[5,3,-3,-2],[5,-2,2,-2],[5,-2,-3,3]])print("计算矩阵的对角化矩阵")P,D = M.diagonalize()print(P)print(D)计算矩阵的对角化矩阵
Matrix([[0, 1, 1, 0], [1, 1, 1, -1], [1, 1, 1, 0], [1, 1, 0, 1]])
Matrix([[-2, 0, 0, 0], [0, 3, 0, 0], [0, 0, 5, 0], [0, 0, 0, 5]])