Visualizing Fourth Dimension

This lecture explores the concept of visualizing the Fourth Dimension by stretching a point into a line, curling it into a circle, twisting it into a sphere, and visualizing the resulting structure. It introduces vector spaces, examples like Q¹, R², and C², and defines a K-vector space as a K-module. The lecture covers vector products, subspaces, linear applications, and morphisms between vector spaces. It discusses linear transformations, isomorphisms, endomorphisms, and automorphisms of K-vector spaces. The lecture concludes with the notation of linear forms and the concept of a linear form on a vector space.