Main concepts of linear algebra

Notions of group, ring, body, vector space, algebra, and in particular tensor algebra, symmetric algebra and exterior algebra (see articles Linear algebra and Calcul tensoriel du traité Sciences fondamentales).

Please refer to these articles for definitions of these fundamental concepts.

The reader must pay attention to the notion of vector (see article Linear algebra) defined in mathematics as an element of a vector space, itself axiomatically defined.

The vectors used by engineers and physicists are often not vectors in the previous sense, but elements of an affine space (i.e., a space translated from a vector space) or vector fields. In particular, from a mathematical point of view, a real function defined on an interval I of