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Python sympy | Matrix.diagonalize () method

Using the sympy.Matrix () method. Diagonalize () we can diagonalize the matrix.  diagonalize () returns a tuple , where diagonally 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 ],

  [< / code> 5 , - 2 , - 3 3 ]])

  

print ( "Matrix: { } " . format (M))

 
# Use the sympy.diagonalize () method

P, D = M.diagonalize () 

 

print ( "Diagonal of a matrix: {}" . format (D)) 

Exit:

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 the method sympy.diagonalize ()

P, D = M.diagonalize () 

  

print ( "Diagonal of a matrix: {}" . format (D))

Exit:

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]])

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