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                <term xml:lang="en">Polynomial matrix</term>
                <term xml:lang="en">Padé approximants</term>
                <term xml:lang="en">Matrix Pencil</term>
                <term xml:lang="en">Minimal base</term>
                <term xml:lang="fr">Approximants de Padé vectoriels</term>
                <term xml:lang="fr">Faisceau de matrices</term>
                <term xml:lang="fr">Base minimale</term>
                <term xml:lang="fr">Matrice polynomiale</term>
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              <p>In this article, we present a new method to compute minimal bases for the kernel of a polynomial matrix. This method uses computation of Padé approximants for the special case where one does not look after an approximation but an exact value. For a polynomial matrix of order $m$ and degree $d$, its cost is about $m^4d^2$ arithmetic operations.</p>
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              <p>Une nouvelle méthode pour calculer une base minimale d'un noyau de matrice polynomiale est présentée. Cette méthode utilise le calcul d'approximants de Padé dans le cas particulier où l'on ne cherche pas une approximation mais une valeur exacte. Pour une matrice polynomiale d'ordre $m$ et de  degré $d$ on trouve un coût de l'ordre de $m^4d^2$ opérations arithmétiques.</p>
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