Linear Transformations: Dimension Theorems

This lecture covers the dimension theorems related to linear transformations, including the Kernel-Image Theorem. It explains how the dimensions of the domain, kernel, and image of a linear transformation are related. The lecture also discusses the criteria for bijectivity and isomorphism between vector spaces of finite dimension. Additionally, it explores the concept of dual spaces and the isomorphism between a vector space and its dual. The lecture concludes with the construction of dual linear transformations and the canonical applications between vector spaces.