  We usually define an algebraic structure by a set, some operations defined on
this set and some propositions that the algebraic structure must validate. In
some cases, we can replace these propositions by an algorithm on terms
constructed upon these operations that the algebraic structure must validate.
We show in this note that this is the case for the notions of vectorial space
and bilinear operation. KEYWORDS: Rewrite system, vector space, bilinear
operation, tensorial product, semantics, quantum programming languages,
probabilistic programming languages.
