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Linear algebra is a basic course followed in mathematics, science, and engineering university departments. Generally, this course is taken in either the first or second year but there have been difficulties in teaching and learning. This type of active algebra has resulted in an increase in research by mathematics education researchers. But there is insufficient information on this subject in Turkish and therefore it has not been given any educational status. This paper aims to give a general overview of this subject in teaching and learning. These education studies can be considered quadruple: a) the history of linear algebra, b) formalism obstacles of linear algebra and cognitive flexibility to improve teaching and learning, c) the relation between linear algebra and geometry, d) using technology in the teaching and learning linear algebra.Mathematics education researchers cannot provide an absolute solution to overcome the teaching and learning difficulties of linear algebra. Epistemological analyses and experimental teaching have shown the learning difficulties. Given these results, further advice and assistance can be offered locally.