The objective of this paper is to establish comparisons between the Linear Algebra (LA) approach practiced in Engineering courses offered by Chilean and Brazilian Higher Education Institutions and, for that, teachers from both countries were interviewed. From a methodological point of view, the research consists of two case studies. For the analysis of the interviews, we used the precepts of Content Analysis. The data were qualitatively analyzed considering the MTSK theoretical model. In this analysis, we sought to identify what specialized knowledge these teachers have regarding AL and about its teaching and learning. The results have shown that, in relation to the Mathematical Knowledge (MK) domain, which refers to content knowledge, the Knowledge of Topics subdomain (KoT), linked to the way that teachers know the topics they teach, is the most present among interviewees. In the Pedagogical Content Knowledge (PCK) domain, covering specific pedagogical knowledge linked to Mathematics, the Knowledge of Mathematics Teaching (KMT), regarding strategies, teaching theories, resources and materials, and Knowledge of Mathematics Learning Standards (KMLS) subdomains, concerning the curricular specifications and the moments in which the student must or can learn certain content and with what level of depth prevail.