Linear Transformations and Matrices

About the project

• Duration: 3-4 hours in class, 1-2 hours preparation at home

• Prerequisites: Basic linear algebra (vectors and matrices, dot product), basic Python programming

• Python packages: numpy, matplotlib

• Learning objectives: Understand matrices as linear mappings \(f(\mathbf{v}) = A\mathbf{v}\), perform matrix–vector and matrix–matrix products in NumPy, interpret the range/image via matrix columns, use rank to reason about invertibility, recognize and construct rotation matrices, understand composition of transformations via matrix multiplication, work with inverse matrices and diagonal matrices, perform change of coordinates between rotated coordinate systems