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]])
