Linear Dependence and Independence: Properties and Criteria

This lecture covers the properties and criteria of linear dependence and independence in a vector space. It discusses the concepts of linearly dependent and independent sets of vectors, along with propositions and proofs related to these concepts. The lecture also explores examples illustrating linear dependence and independence, as well as important properties such as the implications of a set being free or linked. Additionally, it explains the consequences of linear dependence within a collection of vectors and how it affects the overall structure of the vector space.