Advanced Linear Algebra for CS/ML

Advanced linear algebra is the mathematical engine behind modern machine learning, optimization, graphics, and scientific computing.

Why This Section Matters

• Spectral methods and ranking algorithms
• Dimensionality reduction and latent structure
• Stable numerical solving in large systems
• Matrix factorization-based learning methods

Learning Path

flowchart LR
  A[Eigenvalues/Eigenvectors] --> B[Orthogonality and Projections]
  B --> C[SVD and PCA]
  C --> D[Least Squares and Conditioning]
  A --> C

Core Competencies

1. Understand spectral decomposition concepts
2. Use projection geometry for data approximation
3. Apply SVD for compression and denoising
4. Analyze numerical sensitivity in linear models

Exercises

1. Explain relation between orthogonality and numerical stability.
2. Give one ML use-case for each: eigenvectors, SVD, least squares.