Test du plugin WP QuickLaTeX
Voici une équation
and be two polynomials in with matric coefficients
Let us use evaluation with coefficients on the right, that is
Then, if commutes with all the coefficients ,
The proof of this lemma is quite obvious: it is based on the equalities
when commutes with all the
One can apply this lemma to the identity used for the proof,
Obiously, commutes with the left factor
It is then legitimate to replace by in this identity, and we are done.
It is true that commutes also with the matrix coefficients in , but this is not necessary for the proof.
I let it to the author to double-check the reasoning above and to simplify the demonstration acccordingly.
With this simplification, this proof using polynomials with matrix coefficients seems to me the nicest and simplest proof.