Trace of a endomorphism of a finite dimentional vector space
Submitted by Isoscel on Thu, 11/22/2007 - 19:35.
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
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.
Now let be another operator and let consider equation
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Then there is also a relation between associated matrix
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Let
We have
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But so there are no solution for the previous equation on finite dimensional space.