Oxford Linear Algebra - Linear Transformations Explained

Explore the concept of Linear Transformations in this 33-minute video lecture by University of Oxford mathematician Dr Tom Crawford. Delve into the formal mathematical definition of linear transformations and their relationship to vector space properties. Learn about an alternative definition used to verify linearity, and understand how linear maps preserve vector space structure. Examine various examples of linear maps, including matrix multiplication, differentiation, and specific transformations in R3. Discover the application of direct sum in defining projection maps. Gain access to practice exercises and additional video lectures to reinforce your understanding of linear transformations in the context of linear algebra.