Linear Transformations: Kernel and Image

This lecture covers the concepts of kernel and image of a linear transformation, associated with a matrix. It explains how to determine the kernel and image, and their relationship with the rank of the matrix. The lecture also introduces the canonical matrix associated with a linear transformation, providing examples and properties of linear transformations. Additionally, it discusses the uniqueness of the matrix associated with a linear transformation and the application of linear transformations in vector spaces. The lecture concludes with examples of constructing matrices associated with specific linear transformations.