Python | sympy.eigenvals() method

With the help of sympy.eigenvals() method, we can find the eigenvalues of a matrix by using sympy.eigenvals() method.

Syntax : sympy.eigenvals()
Return : Return eigenvalues of a matrix.

Example #1 :
In this example, we can see that by using sympy.eigenvals() method, we are able to find the eigenvalues of a matrix.

# import sympy
from sympy import *

# Use sympy.eigenvals() method
mat = Matrix([[1, 0, 1], [2, -1, 3], [4, 3, 2]])
d = mat.eigenvals()

print(d)

Output :

{2/3 + 46/(9*(241/54 + sqrt(36807)*I/18)**(1/3)) + (241/54 + sqrt(36807)*I/18)**(1/3): 1, 2/3 + 46/(9*(-1/2 + sqrt(3)*I/2)*(241/54 + sqrt(36807)*I/18)**(1/3)) + (-1/2 + sqrt(3)*I/2)*(241/54 + sqrt(36807)*I/18)**(1/3): 1, 2/3 + (-1/2 – sqrt(3)*I/2)*(241/54 + sqrt(36807)*I/18)**(1/3) + 46/(9*(-1/2 – sqrt(3)*I/2)*(241/54 + sqrt(36807)*I/18)**(1/3)): 1}

Example #2 :

# import sympy
from sympy import *

# Use sympy.eigenvals() method
mat = Matrix([[1, 5, 1], [12, -1, 31], [4, 33, 2]])
d = mat.eigenvals()

print(d)

Output :

{2/3 + 3268/(9*(16225/54 + sqrt(15482600967)*I/18)**(1/3)) + (16225/54 + sqrt(15482600967)*I/18)**(1/3): 1, 2/3 + 3268/(9*(-1/2 + sqrt(3)*I/2)*(16225/54 + sqrt(15482600967)*I/18)**(1/3)) + (-1/2 + sqrt(3)*I/2)*(16225/54 + sqrt(15482600967)*I/18)**(1/3): 1, 2/3 + (-1/2 – sqrt(3)*I/2)*(16225/54 + sqrt(15482600967)*I/18)**(1/3) + 3268/(9*(-1/2 – sqrt(3)*I/2)*(16225/54 + sqrt(15482600967)*I/18)**(1/3)): 1}