# Endomorphism/Characteristic polynomial/Well-defined/Exercise

Show that the characteristic polynomial of a linear mapping on a finite-dimensional -vector space is well-defined, that is, independent of the chosen basis.

Show that the characteristic polynomial of a linear mapping ${}\varphi \colon V\rightarrow V$ on a finite-dimensional ${}K$-vector space ${}V$ is well-defined, that is, independent of the chosen basis.