This paper presents the results obtained so far in a long term project developed in Mexico with the purpose of studying in depth students' constructions when they study Linear Algebra at the university level. The goals of the project consist in developing theoretical analyses about the constructions involved in the learning of the different Linear Algebra concepts using APOS theory; validating those analysis by means of empirical research focusing on specific concepts and relationships between them; and making didactic suggestions that can contribute to the teaching of this subject. In particular we present in this study the results obtained for the following concepts: vector space, linear transformation, basis and systems of linear equations.
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