Python同情 | Matrix.diagonalize() 方法

借助sympy.Matrix().diagonalize()方法，我们可以对矩阵进行对角化。对角化（）返回一个元组$(P, D)$ ， 在哪里$D$是对角线并且$M = PDP^{-1}$ .

Syntax: Matrix().diagonalize()

Returns: Returns a tuple of matrix where the second element represents the diagonal of the matrix.

示例 #1：

# import sympy 
from sympy import * M = Matrix([[3, -2,  4, -2],
                                [5,  3, -3, -2],
                                [5, -2,  2, -2],
                                [5, -2, -3,  3]])
  
print("Matrix : {} ".format(M))
   
# Use sympy.diagonalize() method 
P, D = M.diagonalize()  
      
print("Diagonal of a matrix : {}".format(D))  

输出：

Matrix : Matrix([[3, -2, 4, -2], [5, 3, -3, -2], [5, -2, 2, -2], [5, -2, -3, 3]])
Diagonal of a matrix : Matrix([[-2, 0, 0, 0], [0, 3, 0, 0], [0, 0, 5, 0], [0, 0, 0, 5]])

示例 #2：

# import sympy 
from sympy import * M = Matrix([[1, -3, 3], [3, -5, 3], [6, -6, 4]]) 
print("Matrix : {} ".format(M))
   
# Use sympy.diagonalize() method 
P, D = M.diagonalize()  
      
print("Diagonal of a matrix : {}".format(D))

输出：

Matrix : Matrix([[1, -3, 3], [3, -5, 3], [6, -6, 4]])
Diagonal of a matrix : Matrix([[-2, 0, 0], [0, -2, 0], [0, 0, 4]])