### Test du plugin WP QuickLaTeX

Voici une équation

Let

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
code

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.

Le code [latexpage] doit être ajouté manuellement dans la page (ne marche pas s'il est inséré via le modèle de page;
L'ajustement de style suivant est nécessaire pour les formules inline, à cause
d'un styles des images pour les adaptations «responsive», et ce style peut être dans le modèle de page).

<style>
.img-responsive {display: inline;}
</style>