Python sympy | Matrix.diagonalize() method

With the help of sympy.Matrix().diagonalize() method, we can diagonalize a matrix. diagonalize() returns a tuple , where is diagonal and .

Syntax: Matrix().diagonalize() Returns: Returns a tuple of matrix where the second element represents the diagonal of the matrix.

Example #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))

Output:

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]])

Example #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))

Output:

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]])