Linear Forms in Vector Spaces

This lecture covers the definition of linear forms in vector spaces, denoted as V*. It explains how linear forms are linear applications from a vector space V to the field K. The lecture also introduces the concept of the dual space V*, which consists of all linear forms on V. Various properties and proofs related to linear forms and their applications are discussed, including the concept of a generating family in vector spaces and the direct sum of subspaces. The lecture concludes with examples illustrating the theoretical concepts presented.