General Linear Transformations on Vector Spaces

Explore general linear transformations on vector spaces in this 17-minute video lecture. Learn the definition of linear transformations, their basic properties, and how they differ from matrix transformations specific to Euclidean space. Examine various examples and non-examples of linear transformations, including zero transformation, dilation and contraction, inner product transformation, and matrix transformation. Understand why functions like sinx and translation are not linear transformations. Gain insights into linear combinations and proofs of basic properties to deepen your understanding of linear algebra concepts.

Intro
Definition of Linear Transformation
Linear Combinations
Basic Properties
Proofs of Basic Properties
Matrix Transformation
Zero Transformation
Dilation and Contraction
Inner Product Transformation
Matrix Transformation
sinx is not a Linear Transformation
Translation is not a Linear Transformation
Conclusion