Linear Applications of Vector Spaces

This lecture introduces linear applications between vector spaces, defining them as functions from one vector space to another that preserve vector addition and scalar multiplication. The properties and characteristics of linear applications are explored, emphasizing their role in transforming vectors while maintaining linearity. The lecture also covers the concept of bases in vector spaces and how linear applications can be uniquely determined by their action on a basis. The importance of understanding linear applications in various mathematical contexts is highlighted, showcasing their significance in linear algebra and functional analysis.