In [8]:

%load_ext sympy.interactive.ipythonprinting

import sympy as sp

/usr/lib/python2.7/dist-packages/IPython/frontend.py:30: UserWarning: The top-level `frontend` package has been deprecated. All its subpackages have been moved to the top `IPython` level.
  warn("The top-level `frontend` package has been deprecated. "

In [9]:

eps = sp.Symbol("epsilon")
lam = sp.Symbol("lambda")

In [10]:

m = sp.Matrix([[1, eps], [eps, 1]])
m

Out[10]:

$$\left[\begin{smallmatrix}1 & \epsilon\\\epsilon & 1\end{smallmatrix}\right]$$

In [11]:

m.charpoly(lam)

Out[11]:

$$\operatorname{PurePoly}{\left( - \epsilon^{2} + \lambda^{2} - 2 \lambda + 1, \lambda, domain=\mathbb{Z}\left[\epsilon\right] \right)}$$

Observe the occurrence of $(1-\epsilon^2)$ above.