Vector spaces, history and axiomatics
The concept of vector space gradually emerged throughout the 19th century, in order to formalize the space that surrounds us. Visionary pioneers enabled this shift in perspective by introducing the right concepts of « basis », of « dimension », of « determinant », of « linear map »… Linear algebra became the framework for studying numerous theories, particularly in analysis. Today, with the development of computer tools, linear algebra is more easily implemented through matrix computation.
All articles in this folder
A revolutionary concept!
From the geometric motivations of the earliest scholars to its axiomatization around 1900, the concept of a vector space was gradually refined into the indispensable foundation of many mathematical theories. Here is its thrilling story.
First examples of vector spaces (1)
Before we get to the heart of the matter, it is worth remembering that we have all encountered a vector space at school.
Latin, a source of new words – maths brief | Tangente
The development of linear algebra gave rise to new terms, such as "scalar", and revived others, such as "vector".
The determinant: an essential tool in linear algebra | Tangente
The determinant provides a criterion for determining whether an endomorphism is bijective. Its geometric interpretation also tells us about the nature of linear transformations.
“The” dimension: not such an obvious idea!
The notion of dimension can be glimpsed in Euclid, then takes clearer shape with Descartes before branching out according to the subject at hand: analytic geometry, vector spaces or topology. There is a whole host of “dimensions”! Here, the focus is on the dimension of vector spaces, due to Georg Hamel.
Linear maps: the "hard core" of linear… algebra
Linear maps are an essential concept in the theory of vector spaces. They have many uses, including designing and solving games.