## Trace of a endomorphism of a finite dimentional vector space

Posted November 22nd, 2007 by Isoscel

Let X be a n-dimensional k-vector space over a complete field k and The spectrum of is formed by n eigenvalues .

We call .

From "Matrix representation of linear operator" there is a matrix associated with the linear operator and are solutions of equation and after a short calculation we have

.

Now let be another operator and let consider equation

Then there is also a relation between associated matrix

Let

We have

But so there are no solution for the previous equation on finite dimensional space.