Past exam of the algebra, analysis and differential equations II course of the University of Oxford / 2011 / Algebra / 1 / a

Choose a basis and let $A$ represent $T$. Define the characteristic polynomial byUnder a change of basis with invertible change matrix $S$, the new matrix is $S^{-1}AS$. HenceThus the polynomial is independent of the chosen coordinates. It is monic of degree $\dim V$.