Module 8: Applications of Linear Algebra
See linear algebra in action: change of basis, the singular value decomposition, principal component analysis, and computer graphics transformations.
Module Lessons
1
Change of Basis and Similar Matrices
Understand transition matrices, similarity, and why changing basis simplifies problems.
2
Introduction to the Singular Value Decomposition
Factor any matrix as A = U Sigma V^T, compute SVD for small matrices, and understand its geometric meaning.
3
PCA and Dimensionality Reduction
Use eigenvalues of the covariance matrix to find principal components and reduce dimensionality.
4
Computer Graphics: Rotations, Scaling, and Projections
Apply transformation matrices to computer graphics, including homogeneous coordinates and composing transforms.