Geometry and Linear Algebra

Abstract

No beginner’s course in mathematics can do without linear algebra. According to current international standards it is presented axiomatically. It is a second generation mathematical model with its roots in Euclidean geometry, analytical geometry, and the theory of systems of linear equations. This brings pedagogical difficulties. Beginners with a shaky background in geometry and algebraic computation who also have difficulties with abstractions are really not ripe for the study of linear algebra. On the other hand, there is no need to exaggerate the difficulties. The theory is very simple, has few theorems and is free from complicated proofs. It is also a must. Not being familiar with the concepts of linear algebra such as linearity, vector, linear space, matrix, etc., nowadays amounts almost to being illiterate in the natural sciences and perhaps in the social sciences as well.