In [1]:

    

from sympy import *
init_printing()


    

In [2]:

    

A = Matrix([[4, -10], [2, -4]])
A


    

    
Out[2]:





$$\left[\begin{matrix}4 & -10\\2 & -4\end{matrix}\right]$$

In [3]:

    

lamda = symbols('lamda')
p = A.charpoly(lamda)
factor(p)


    

    
Out[3]:





$$\lambda^{2} + 4$$

In [4]:

    

A.eigenvals()


    

    
Out[4]:





$$\left \{ - 2 i : 1, \quad 2 i : 1\right \}$$

In [5]:

    

simplify(A.eigenvects())


    

    
Out[5]:





$$\left [ \left ( - 2 i, \quad 1, \quad \left [ \left[\begin{matrix}\frac{10}{4 + 2 i}\\1\end{matrix}\right]\right ]\right ), \quad \left ( 2 i, \quad 1, \quad \left [ \left[\begin{matrix}\frac{10}{4 - 2 i}\\1\end{matrix}\right]\right ]\right )\right ]$$