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Linear Transformations: Matrices and Applications
This lecture introduces linear transformations, focusing on interpreting matrices as linear applications that act on vectors. It covers the concept of linear independence, canonical bases, and the interpretation of matrices as transformations. The lecture also discusses the properties of linear transformations, such as linearity and the transformation of vectors. Additionally, it explores the association of matrices with linear transformations, emphasizing the importance of respecting the order of components in bases. The lecture concludes with practical examples illustrating the application of linear transformations in systems of equations and ordered lists.