Linear Transformations: Matrices and Applications

This lecture covers the concept of linear transformations and their representation through matrices. It explains how to associate a matrix with a linear transformation, the properties of injective, surjective, and bijective transformations, and the equivalence between these properties and properties of the associated matrix. Additionally, it discusses matrix operations, such as matrix addition and scalar multiplication, along with special types of matrices like null matrices, diagonal matrices, and identity matrices.