Trace of a endomorphism of a finite dimentional vector space
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
But so there are no solution for the previous equation on finite dimensional space.