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pythonmatrixsystemsympy

How to find the eigenvalues and eigenvectors of a matrix with SymPy?

I want to calculate the eigenvectors x from a system A by using this: A x = λ x

The problem is that I don't know how to solve the eigenvalues by using SymPy. Here is my code. I want to get some values for x1 and x2 from matrix A

from sympy import *
x1, x2, Lambda = symbols('x1 x2 Lambda')
I = eye(2)
A = Matrix([[0, 2], [1, -3]])
equation = Eq(det(Lambda*I-A), 0)
D = solve(equation)
print([N(element, 4) for element in D]) # Eigenvalus in decimal form
print(pretty(D)) # Eigenvalues in exact form

X = Matrix([[x1], [x2]]) # Eigenvectors
T = A*X - D[0]*X # The Ax = %Lambda X with the first %Lambda = D[0]
print(pretty(solve(T, x1, x2)))
Solution

  • sympy has a very convenient way of getting eigenvalues and eigenvectors: sympy-doc

    Your example would simply become:

    from sympy import *
A = Matrix([[0, 2], [1, -3]])
print(A.eigenvals())  #returns eigenvalues and their algebraic multiplicity
print(A.eigenvects())  #returns eigenvalues, eigenvects