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.