Welcome to our comprehensive guide on linear transformations! Dive into the fascinating world of linear algebra and explore the incredible applications of linear transformations.
What is a Linear Transformation?
A linear transformation is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication. These transformations are represented by matrices and have the form:
- Additivity: T(u + v) = T(u) + T(v)
- Homogeneity: T(cu) = cT(u)
Applications
Linear transformations are widely used in various fields such as computer graphics, data science, and engineering. Some key applications include:
- Rotations and reflections in computer graphics
- Data transformation and feature scaling in machine learning
- Solving systems of linear equations
Interactive Examples
Check out these interactive resources to see linear transformations in action: