Matrices for General Linear Transformations - Linear Algebra

Explore the concept of transformation matrices for general linear transformations between vector spaces in this 18-minute educational video. Learn how to translate vectors to coordinates, multiply coordinate vectors by transformation matrices, and revert back to vectors in the codomain. Derive the formula for transformation matrices in finite-dimensional linear transformations and examine various examples involving matrices for linear transformations. Gain insights into matrix operations, coordinate systems, and the practical applications of transformation matrices in linear algebra.

Intro
How the Matrix Works
Finding the Transformation Matrix
What is the Transformation Matrix
Finding a Transformation Matrix
Using Transformation Matrix
Multiple Matrices for one Transformation
Conclusion