We present an epistemological and didaccical analysis of students' difficulties en linear algebra as taught in first year of French science university. We deduce from it hypotheses for research work. We present an engineering for chis ceaching based on these hypotheses. This engineering takes the form of a long-term project (over one year) and uses, to a great extent, the "meta lever" and the changes of setting and points of view. The evaluation currenrly in progress of the project draws on certain methodological difficulties encountered in the validation of the type of hypotheses which have been made.